[0001] The section headings used herein are for organizational purposes only and should not be construed as limiting the subject matter described in the present application in any way.

Introduction

[0002] Systems that exchange information using single photons are useful for a wide variety of computing, communication, and measurement applications. One example of such systems are systems that use photon phase correlation to perform sensing and measurement.

This includes quantum LiDAR, quantum imagers, quantum HOM interferometers, quantum OCT and various other optical measurement systems. For these systems, the sharing of classical state information, quantum state information, and various hybrids of these can be used to increase accuracy, precision, and speed of data taking as compared to purely classical systems. As such, methods and systems that support and improve state information transfer using single photons is useful in advancing the state-of-the art. Of particular interest currently are systems that exploit time correlation cross sets of photons that number more than two.

Brief Description of the Drawings

[0003] The present teaching, in accordance with preferred and exemplary embodiments, together with further advantages thereof, is more particularly described in the following detailed description, taken in conjunction with the accompanying drawings. The skilled person in the art will understand that the drawings, described below, are for illustration purposes only. The drawings are not necessarily to scale; emphasis instead generally being placed upon illustrating principles of the teaching. The drawings are not intended to limit the scope of the Applicant’s teaching in any way.

[0004] FIG. 1 illustrates an embodiment of a source that generates time-correlated quadruplets of single photons.

[0005] FIG. 2A illustrates an embodiment of a system for generating and measuring time-correlated quadruplets of the present teaching.

[0006] FIG. 2B illustrates measured event lists that can be used for some embodiments of a system and method of sharing quantum information using time-correlated single photons of the present teaching.

[0007] FIG. 2C illustrates a schematic diagram of entangled photon sets for embodiments of a system and method for sharing quantum information using time-correlated single photons of the present teaching.

[0008] FIG. 2D illustrates an embodiment of a receiver for measuring a pair from time- correlated quadruplets of the present teaching.

[0009] FIG. 3A illustrates an embodiment of a system for sharing quantum information using time-correlated single photons generated by a SPDC source of the present teaching.

[0010] FIG. 3B illustrates a table of cases for an event list associated with an embodiment of the system for sharing quantum information using time-correlated single photons of FIG. 3 A.

[0011] FIG. 3C illustrates a table of lost photons and false coincidences for an embodiment of the system for sharing quantum information using time-correlated single photons of FIG. 3 A.

[0012] FIG. 4 illustrates an embodiment of a system for sharing quantum information within a single node using time-correlated quadruplet identification of the present teaching.

[0013] FIG. 5 illustrates an embodiment of a system for sharing quantum information of the present teaching that includes HOM-dip measurement.

Description of Various Embodiments

[0014] The present teaching will now be described in more detail with reference to exemplary embodiments thereof as shown in the accompanying drawings. While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. Those of ordinary skill in the art having access to the teaching herein will recognize additional implementations, modifications, and embodiments, as well as other fields of use, which are within the scope of the present disclosure as described herein.

[0015] Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the teaching. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment.

[0016] It should be understood that the individual steps of the methods of the present teachings can be performed in any order and/or simultaneously as long as the teaching remains operable. Furthermore, it should be understood that the apparatus and methods of the present teachings can include any number or all of the described embodiments as long as the teaching remains operable.

[0017] Quantum entanglement is a powerful resource that has numerous applications in a variety of processing, sensing and communications applications. One important and basic requirement for the efficient and effective use of quantum entanglement is the need to quickly and/or easily identify the entangled resources. For example, each photon in a pair of entangled photons can carry state information that is entangled such that the values of those states are the same when measured. As such, it is necessary to identify photons that are part of a pair of entangled photons in order to know that a particular measured value is one of two shared correlated values.

[0018] Generally, each photon in a set of entangled photons can carry state information that is entangled such that the values of those states are the same when measured. For optical measurement applications, the correlation of entangled photons, specifically in a phase dimension and/or a time dimension, can produce very precise time and/or position measurements. In addition, for optical measurement applications, the non-local correlation of entangled photons can be used to provide a point-to-point image correlation between optical detections at an object plane and an image plane. These applications require the timely and accurate identification of photons that are part of a set of entangled photons in order to know the measurements using the photons of the set are correlated.

[0019] Systems and method for identifying photon sets that are entangled, and the corresponding measured state values that are correlated, is notably different from classical resource identification systems or methods. This is particularly true when the classical systems and methods used for optical measurement systems because these systems typically produce, process and detect large numbers of photons. Some of the differences arise, at least in part, because a measurement of a photon collapses the associated quantum states in an irreversible way. Also, some of the differences arise, at least in part, because quantum resources can be quantized where their states take on only specific and/or singular values that are not characteristic of large numbers of photons and associated analog opto-electronic detection of those photons. Furthermore, some of the differences arise because entangled resources carry perfectly correlated state information. Differences can arise because of various combinations of these qualities.

[0020] Another important difference between identifying classical data sets and identifying entangled photons and their associated correlated state values arises because many well-known, low cost, sources of entangled photons generate orders of magnitude more photons that are not entangled compared with photons that are entangled. Other photon sources that are not entangled could be, for example, ambient light, purposeful interference from a 3 ^rd party, and noise in any channel between the source of the photons and detectors. Consequently, for many practical systems, the photons that are not entangled must not be erroneously identified as entangled. This results in a kind of high background condition. Quite different from classical situations, it is possible to find and process quantum information that is surrounded by very high backgrounds. In contrast, classical optical detection and measurement systems reach a point where it is not possible to detect and process an optical image or other signal once the signal level falls sufficiently below a noise level. The entangled photon identification method and system of the present teaching can operate when a number of legitimate entangled, correlated photons in a measurement window is multiple orders of magnitude less than a number of nonentangled background photons or background counts from other sources in that same measurement window. In fact, many engineering design “rules of thumb” that are commonly accepted for classical imaging and measuring systems do not apply, or serve to limit, similar quantum versions of those imaging and measuring systems. This can be true even if the classical apparatus and quantum apparatus share the same, or similar, physical structure.

[0021] Entangled photon identification is also subject to lost photons. A lost photon in an entangled set of photons can create an error condition that can be exhibited after measurements. There is an expectation that a correlated state value at one location from measurement of one of the photons in the set has a correlated pair state value at a second location from measurement of another photon in the set, and when this measured state value is not present, an error in the correlated data sets occurs.

[0022] For purposes of describing the present teaching, we describe two different forms of quantum information: quantum information in a quantum form and quantum information in a classical form. Quantum information in a quantum form includes quantum information in a potential state. Some refer to a potential quantum state as “res potentia”, that is, offering possibilities. Examples of a potential state include a coherent state, a superposition state and an entangled state. In some cases, a potential quantum state is a state that is unknown and/or not yet measured. We also use the term quantum information to include information in a classical form.

This quantum information can include information in a measured or collapsed state. This kind of quantum information is, for example, the outcome of a measurement of potential state the yields a particular state value (e.g. one of the possible superposition states). We also use the term quantum information in a classical form to include wavefunction information that can be a deterministic description that bounds and/or provides the evolution of a potential state of a quantum system.

[0023] Although both the measured states and the wavefunction information are quantum information, they differ from the potential state information in that they are classical in nature. For one thing, they are actual or known. Also, they can be communicated over classical channels and used and/or processed by classical information systems, including classical memory, CPU, analog and/or digital processors, and a variety of classical sensing and measurement systems that may be analog and/or digital in nature, without any fundamental change to their properties.

[0024] It is important to emphasize that quantum information in a quantum form has certain quantum properties, e.g. quantization, superposition, non-locality, correlation and combinations of these qualities. A quantum potential state description applies when the system is coherent or still in superposition. A notable quality of the potential state is that at least some of the quantum state information is not known. Once the carriers of quantum state information in a quantum form, e.g. photons, atoms, ions, and superconducting junction currents, are measured to yield the quantum state information, the states of those carriers are collapsed, and therefore yield measured quantum state information in a classical form. This measured quantum state information is classical in nature, and can be further processed in a classical way, but yet it is intimately connected to the quantum nature of the potential state that was measured, and this is why it is referred to as quantum information. As examples, non-locality, and correlation properties are characteristic of quantum information in a classical form. These properties are not possible with purely classical information derived from classical systems. [0025] In addition to the above description of the different forms of quantum information, quantum and classical, it is important to consider how the systems and applications use the quantum information. Some applications and systems that use quantum information use a portion of the quantum information they intake to directly process, store, measure, sense and/or communicate. It is convenient to refer to this portion of the quantum information as the quantum data. Another portion of the quantum information the applications and systems intake is used to aide in the processing, measuring, sensing and/or communicating of the quantum data. It is convenient to refer to this portion of the quantum information as the quantum metadata.

[0026] The quantum data and quantum metadata terminology is analogous to the use of the term metadata in information technology as referring to information about the data, as opposed to the data itself. It should be understood that the portion of quantum information that is considered quantum data and the other portion of quantum information that is considered quantum metadata is determine at least part by the application or system that is using the quantum physical system. It should also be understood that whether quantum information is in a classical form or a quantum form is determined at least part by to the particular quantum physical system. It is important to understand that the definitions or categorizations of what information is quantum metadata and what information is quantum data can change from one application to another, or for different operations within the same application.

[0027] References herein to classical information include information that can be used by classical information systems. As such, this includes general classical information that is naturally or by its origin in a classical form and can also include quantum information in a classical form. [0028] The method and system of the present teaching addresses a need for efficiently and accurately identifying entangled resources for optical measurements that use single photons. However, it should be understood that the teaching is not intended to be so limited. As understood by those skilled in the art, aspects of the teaching can apply to resources of numerous entangled systems including, for example, entangled atomic systems, ionic systems, spin systems, superconducting systems, quantum dots, and other systems. In these cases, the quantum state information, and associated quantum metadata concepts remain the same, but the physical system that carries the state, as well as in some cases the different entangled bases, is different as understood by those skilled in the art. The teaching can also be applied to hybrids of these and other systems.

[0029] Single photons are a powerful resource that carries correlated timing, phase and position information that can be used in a variety of quantum and/or classical systems that measure time, position, distance, phase and other related parameters. Specifically, it is known that interferometric systems can benefit from quantum optical states. For example, the Laser Interferometry Gravitation-Wave Observatory (LIGO), Light Distance and Ranging (LiDAR), optical coherence tomography, optical interferometric imaging can benefit from optical quantum states as can numerous other optical image measurement systems.

[0030] Single photons are indivisible particles and consequently their measurement is unique and well-defined. This leads to desirable features including privacy, security, tolerance to third party meddling and/or snooping, and quantization features useful for various communication, computing, and sensing applications.

[0031] At the same time, various optical sources are available and currently in development that can generate two, or more, entangled photons at a same time. For example, spontaneous parametric down conversion (SPDC) generates pairs of single photons at a same time. Some configurations of SPDC, for example, those that use forward and backward pumping, can generate four photons at a same time. Processes, such as four-wave mixing and Raman can also be used to generate pairs, triplets and/or quadruplets of photons that are all generated at a same time. In many cases, the time correlation is owed to time-energy entanglement processes. We may refer to these entangled sets of single photons as time- correlated photon sets or sets of entangled photons. There can be any number of time correlated photons in a set. A set of four entangled photons may be referred to as a quadruplet. Multiple sets of entangle photons are typically generated by an optical source over time. The number of sets per second is referred to as the generation rate. Spontaneous parametric down conversion sources, and many other down conversion and nonlinear sources can be configured to generate multiple sets of entangled photons over time. Some random or spontaneous processes generate streams of these time-correlated photon sets such that the time between arrivals of the time- correlated photons is governed by random processes and so the arrival times of these photon sets, and the inter-arrival time between photon sets, are correlated random values.

[0032] A common challenge with using the properties of the entangled time-correlated photon sets is that the time-correlated photons are typically surrounded in, e g., time and space, by high levels of background photons, which is essentially noise. Low-cost sources, such as SPDC sources, typically generate more photons that are not time-correlated than photons that are time correlated. Furthermore, photons are measured using detectors that produce substantial levels of background signals in addition to actual photon measurements. One feature of the present teaching is the ability to identify time-correlated photons amidst high levels of noise, which includes photons from sources that are not correlated, and background signals with a minimum amount of computation and hardware.

[0033] Thus, one feature of the present teaching is that time correlations of entangled single photons having non-local properties can be exploited in measurement systems to achieve new functionality and/or improved performed metrics as compared to classical versions of these measurement systems and also as compared to known quantum versions of these measurement systems. In particular, using time correlations of entangled single photons according to the present teaching can achieve performance improvements in synchronization, reduction of noise and/or background resilience, and/or measurements of time and space that rely on quantum state information exchange. These performance improvements can be robust to high background counts.

[0034] Various sources support generation of single photons, including time-correlated single photons, that are entangled in various distinguishable bases. Entanglement of photons refers to photons that share quantum state information such that measurements of each photon in one or more bases, even if performed at different times and/or places, yields measured quantum states in each basis that are perfectly correlated. Sometimes these states in each basis are referred to a superposition states. Example bases include time-energy, spatial position, momentum, polarization, wavelength and phase. For measurement applications, time-energy and phase bases are particularly useful.

[0035] Time-energy entangled photons possess a continuum of entangled time probabilities defined by their probability wavefunction, which we may refer to as a time wave packet. The probabilistic nature of the time-correlated value can be exploited if sub-wavepacket time resolution is used. Even with lower time resolution, the correlation can be exploited to find correlated photons precisely and/or within large background environments. In addition, many entangled photon generators rely on stochastic processes that are themselves random, allowing time-correlated photons to carry random time information based on those processes. These features are exploited in various ways for measurement schemes that use embodiments of the time-correlated photon identification system and method of the present teaching.

[0036] Position-momentum entangled photons possess a continuum of entangled position probabilities defined by their probability wavefunction, which we call a position wave packet. The probabilistic nature of the position-correlated value can be exploited if sub-wavepacket spatial resolution is used. Even with lower spatial resolution, the correlation can be exploited to find correlated photons in space precisely and/or within large background environments. In addition, many entangled photon generators rely on stochastic processes that are themselves random, allowing position-correlated photons to carry random yet correlated position information based on those processes. These features are exploited in various ways for measurement schemes that use embodiments of the time-correlated photon identification system and method of the present teaching.

[0037] One feature of embodiments of the system and method of the present teaching is the ability to identify time-correlated photons without relying on complex, high-resolution time synchronization schemes within the system sharing information. Numerous entanglement experiments use time coincidence counters to verify entanglement and validate the Bell inequality. These experiments rely on time coincidence for entanglement generated by spontaneous parametric down conversion as a valid determinant of entanglement and identification of photons that can carry other entangled state information. However, coincidence counters can be difficult to use in practice. In prior art systems, high-resolution time synchronization is needed. For example, even the length of the wire or propagation time between the detector and the counter can skew timing. The future success of transition of quantum systems to practice demands systems and methods that can allow the use of quantum “coincidence” detection schemes that practically work in real life systems outside of controlled lab environments. The system and method of time-correlated photon identification of the present teaching can address many of these challenges. Some basic operations and examples of the use of time-correlated photons for the identification of quantum information are described in U.S. Patent Application Nos. 18/167,589, 18/167,633, and 18/167,670, filed on April 10, 2023, which are all incorporated herein by reference and assigned to the present assignee.

[0038] One feature of the present teaching is that it can use high-brightness single-photon sources to generate time-correlated photons. Some high-brightness sources create large numbers of quantum-entangled, time-correlated photons using Spontaneous Parametric Down Conversion (SPDC). SPDC relies on laser-pumped nonlinear crystals in various configurations. The pumped crystals emit photons that are time correlated. The crystals can also be configured to emit entangled photons in one or more basis which can include polarization, frequency (color) and/or spatial position. The state of a photon emitted in this multi-dimensional quantum state can be measured and represented as having an arrival time, a position, a frequency and/or a polarization.

[0039] One example case is a source that generates sets of four time-correlated photons.

In addition to the quadruplets, these sources can also emit pairs and singles that are not part of a quadruplet. FIG 1 illustrates an embodiment of a source 100 that generates time-correlated quadruplets of single photons. A pump laser 102 generates pump light 104 incident on a nonlinear crystal 106. In some embodiments, the source 102 and crystal 106 are configured in a type-II down conversion arrangement. A mirror 108 reflects some of the pump light 104 back toward the crystal 106. In some embodiments, the pump laser 102 is a blue and/or UV laser and the crystal 106 is a Beta-Barium Borate (BBO) or Bismuth Borate (BiBO) crystal. More details of an example of such a source can be found in the reference, Nikolai Kiesel, Christian Schmid, Ulrich Weber, Geza Toth, Otfried Guhne, Rupert Ursin, and Harald Weinfurter, “Experimental Analysis of a Four-Qubit Photon Cluster State,” Phys. Rev. Lett. 95, 210502, 2005.

[0040] It should be understood that the source 100 of FIG. 1 is just one particular example of a source that can be used with systems according to the present teaching. Many types of single photon sources can be utilized, for example, sources that use Type-I and type-0 phase matching, sources that use periodically poled crystals, including lithium niobate and doped lithium niobate poled crystals, and/or sources that rely on nonlinear processes in optical fibers. A variety of crystals and nonlinear materials can be pumped using infrared laser sources, which can be configured, for example, to emit photons in the infrared at wavelengths that are compatible with optical fiber transmission with low loss.

[0041] The source 100 can generate four photons simultaneously that emerge in particular directions, labeled a l lO, b 112, c l l4 and d 116 in FIG. 1, resulting in a quadruplet of time-correlated photons. The emergence angle, or emission direction, is set by a phase matching condition in the crystal 106. It is also possible that pairs of photons can emerge simultaneously along directions a 110 and b 112, which is referred to as forward directions, or direction c 114 and d 116, which is referred to as backward directions, without being part of a quadruplet.

However, it is very unlikely that photons will emerge along one forward direction, a 110 or b 112 and one backward direction, c 114 or d 116, simultaneously without being part of a quadruplet. Therefore, the coincidence of any forward direction photon with a backward direction photon can herald a quadruplet with very high probability. This means that by appropriately configuring coincidence determination between different pairs of this particular kind of quadruplet allows identification of quadruplets with high fidelity. The table 118 shows some examples that a coincidence pair from directions a-c indicates a presence of photons from directions b-d in a time-correlated quadruplet, as does a coincidence of b-d photons imply a correlated coincidence of a-c photons. It should be understood that a coherence length of the pump 102 must be sufficiently long that the forward propagating field and the backward propagating field from mirror 108 are coherent at the crystal 106 for proper operation. It should be understood that generally quadruplets of the present teaching can effectively arise from either so-called double pair emission and from coherent generation of forward and backward pairs in the crystal 106.

[0042] In some embodiments, a metadata collector 120 is used to generate metadata about the quantum states. For example, the metadata collector 120 can be connected directly to the pump source 102 and/or to the optical output of the pump 102. The metadata collector can determine a pulse shape and repetition rate that can be used to determine time-windows where the entangled photons may be found. The metadata collector 120 can determine other information that relates to the quantum states generated by the interaction of the pump in the crystal 106, including for example, polarization, power, pulse width, amplitude and phase noise, and other information about the pump that contribute to the quantum states that are generated.

[0043] In some embodiments, the metadata collector 120 is collecting wavefunction information about the quantum states being generated in the crystal. For example, the metadata collector 120 determines specifics of the optical signals and the associated modes that pump the crystal 106 that yields information about when, where, and in what spatial condition, the entangled photons emerge from the crystal. As a simple, but important example, during time periods when there is no pump signal applied to the non-linear crystal, no entangled photons will emerge. Other examples of wavefunction metadata that can be collected include, for example, polarization, frequency, and phase properties of the photons as well as deterministic time windows of their emergence.

[0044] We refer to pairs of a quadruplet that provide a higher probability of indicating a quadruplet as preferred pairs. We note that the description herein of high-fidelity indication of quadruplets by measurement of preferred pairs is provided for coincidences of photons that emerge from a crystal in different directions, forward and backward. Specifically, a forward emerging photon and a backward emerging photon are a preferred pair. However, systems and methods of the present teaching are not so limited. Generally, systems of the present teaching can utilize coincidence measurements of pairs of a quadruplet which herald that quadruplet with a high probability (such as with preferred pairs) as compared to measurements of different pairs of that same quadruplet. This would be true, for example, for systems that had certain phase matching conditions that were specific to the quadruplet generation and not shared with phase matching conditions of pair generation. Additionally, some embodiments do not have preferred pairs generated, and/or do not use preferred pairs, and, thus, coincidence of any pair in the quadruplet can be used to identify the quadruplet. This can be done, for example, using sources that produce low background rates of singles and/or pairs together with producing quadruplets at a high rate.

[0045] One feature of the present teaching is the realization that identification of pairs from a quadruplet can be used to identify all members of the quadruplet. This allows sharing of quantum information associated with measurements of photons in that quadruplet. The sharing can include exchanging of information from measurements of the entangled resources that is arranged in ordered lists. These lists can be the same or similar to lists that are used to identify entanglement and share quantum information using entangled pairs of photons. Some example identification methods and systems, and also associated applications that utilize identification, have been disclosed in U.S. Patent No. 11,614,771, entitled “Method for Synchronizing and Locking Clocks”, which is incorporated herein by reference and assigned to the present assignee. It is important to note that some embodiments of the present teaching do not generate lists at all, and rather the photon measurements and/or coincidence measurements are used in nominally real time, rather than being arranged and stored in lists for post processing. However, many properties of the elements of lists and associated correlation properties carry over to the real-time operation. Examples of real time operation include a local finding of a coincidence pair in a set that is used immediately or simultaneously to direct a measurement or read or store a value associated with measurement of another photon or pair of photons in that same set.

[0046] It should be understood that while configurations for identifying quadruplets based on pairs is described herein, the present teaching is not so limited to this aspect of the description. Using the methods and apparatus of the present teaching, subsets of various numbers of photons comprising sets of various numbers of time-correlated photons can be used to identify the sets of time-correlated photons.

[0047] FIG. 2A illustrates an embodiment of a system for generating and measuring time-correlated quadruplets of the present teaching. A time-correlated photon source 202 generates four time-correlated photons that emerge at four outputs and follow four paths, 204, 206, 208, 210 to four detectors 212, 214, 216, 218. The paths 204, 206, 208, 210 can be free space paths or any type of guided paths, such as ones guided by optical fibers and other types of optical waveguide. Two detectors 212, 214 are connected to coincidence detector 220, and two other detectors 216, 218 are connected to another coincidence detector 222.

[0048] In the system 200, the source 202 produces four photons simultaneously. In some embodiments, two of the photons are directed to one location that includes the two detectors D1A 212 and D2A 214, and two photons are directed to a second location that includes two detectors DIB 216 and D2B 218. There is at least one local coincidence detector 220 at the location that includes DI A 212 and D2A 214, and a second local coincidence detector 222 at the location that includes two detectors DIB 216 and D2B 218. In some embodiments, the local coincidence detector can be as simple as a AND logic gate.

[0049] When the coincidence detector 220 finds a local coincidence at the location that includes D1A 212 and D2A 214 (in other words, determines there are simultaneous detection events at D1A 212 and D2A 214), a time-correlated photon pair has arrived. We note that the description assumes equal time-of-flight (TOF) from source 202 to detectors 212, 214, 216, 218 of each photon. The time correlation of sets of entangled photons ensures that when the location that includes D1A 212 and D2A 214 detects a local coincidence, the location that includes two detectors DIB 216 and D2B 218 will also detect a local coincidence. As mentioned before, much of the description herein assumes that latency from source to detector(s) is managed such that “coincidence” is synonymous with simultaneity.

[0050] In some embodiment, systems and methods according to the present teaching compensate for arrival delays resulting from the speed of light. As understood by those skilled in the art, various known approaches to addressing differences in latency from source to measurement can be used in keeping with the systems and methods for identifying time- correlated photons in distributed systems of the present teaching. For example, if the time-of- flight is longer on link 204 than 206, or longer on link 208 than 210 than a known amount, the coincidence detector can be preceded by an appropriate fixed time delay in the connection between DI A or DIB to the coincidence detector. So more generally, the concept of coincidence embodied herein allows for the use of known methods and systems at the receivers and receiver nodes that correct for any time-of-flight different, detection time difference, or any other differential latency in the system that is delivering and measuring the photons that carry the quantum correlated states. Accordingly, in some embodiments, systems and methods of identifying time-correlated photons can be used to determine and correct some latency differences from source to detector(s). That is, identifying time-correlated photons includes compensating for time delays the determination of the coincidence. This can include, for example delays such as time-of-flight delays, detection latency, circuit latency, signal processing delays, optical measurement latency, etc.

[0051] Because the location that includes D1A 212 and D2A 214 detecting a local coincidence means the location that includes two detectors DIB 216 and D2B 218 will also detect a local coincidence, the two locations can each construct ordered lists of measurements of time-correlated events that match without exchanging any classical data. No common quantum state basis is needed to identify coincidences. In some embodiments, times between arrivals of time-correlated photons is used to produce a shared random number, and there is no need to share any information between locations to accumulate the shared number. In some embodiments, measurements of additional entangled basis information carried by the time- correlated photons is shared information and there is no need to exchange any information between nodes to accumulate this shared entangled state information. For example, polarization and/or position information can be shared in this way. Such embodiments can provide a high level of security.

[0052] In some embodiments, one or both of the coincidence detectors 220, 222 are connected to a processor 226, that can be one processor or multiple processors that can be distributed. This configuration supports the processor 226 generating event lists that include coincident determinations from one or both of the coincidence detectors 220, 222. Those lists may be formulated as time stamps, marks in time bins, or other formats. In some embodiments, one or more of the detectors 212, 214, 216, 218 are connected to the processor 226 (only one connection shown). This configuration supports the processor 226 generating event lists that include single photon detection measurements, that would typically also include background counts events, of the one or more of the connected detectors 212, 214, 216, 218. Those lists may be formulated as time stamps, marks in time bins, or other formats. Those lists may be in order of arrival time, as referred to as ordered event lists or lists of ordered measured events.

[0053] In some embodiments, one or more of the photon source 202, one or more detectors 212, 214, 216, 218 (only one connection shown), one or two coincidence detectors 220, 222 (only one connection shown) can be connected to a metadata collector 224 that is connected to processor 226. This supports the processor 226 generating metadata information lists. The lists can include, for example, one or more of number of coincidences in a time window, timewindows of expected entangled pairs based on pump pulse information, background counts or expected background levels based on detector bias point, measurement start and stop times in some coordinated time frame, quantum state coherence levels (including deterministic and probabilistic values or estimates), various wavefunction information, and many other kinds of information.

[0054] A distinction is made in this disclosure between metadata, which is information about the quantum states, and quantum state measurement information or values (quantum data), in that a quantum measurement collapses the quantum state, whereas metadata can some cases be collected without collapsing the state. An example of the use of a combination of metadata and quantum state information, is to allow quantum privacy of a superposition basis of an entangled system to be kept locally, while other information is shared publicly to support privacy and security applications. As another example of the use of a combination of metadata and quantum state information, multiple different kinds of entanglement sharing applications can be used to identify entanglement while sharing small amounts of data about the entanglement.

[0055] In some cases, the measured quantum state information can carry a high capacity or density of information, for example, if it is part of a high-dimensional quantum basis, and the minimum information exchanged required to “tap” this capacity is relatively small. As one particular example, a number of coincidences, which is a single number, can be used to verify one or any number of precisely measured time-entangled photon. Also, the resulting shared timestamp values that represent the measured quantum state value of these entangled photons can represent a large set of information, depending on the application.

[0056] It is important to note the generality of the sharing of the metadata and the sharing of the quantum entangled states of the present teaching. Different applications would construct and use different combinations of these measurements, lists and sharing methods in different ways. Some examples are presented herein. However, it will be clear to those skilled in the art that numerous systems and methods can benefit from and use the association of the metadata and the measured quantum state data to share and derive quantum entangled state information. For example, the method and system according to the present teaching is applicable to distributed systems, localized systems, and hybrids of localized and distributed. The methods and systems according to the present teaching can be applied to privacy systems, key distribution systems, measurement systems, coding and communication systems, location systems, synchronization systems and many other kinds of systems that can use entangled quantum state information. Embodiments of the system and method that use the associated metadata can, for example, reduce information sharing requirements, enhance privacy and security, improve accuracy, reduce latency, and/or support high background count operations while sharing quantum state information as compared to systems that rely on sharing of quantum state information alone.

[0057] In some embodiments, lists of measurement event information generated in two separated locations that is associated with the coincident photons determined in each location is shared information between those locations with no classical information exchange. The lists can include, for example, arrival times of coincidence photons. The lists can be ordered by time of arrival. A feature of using these lists of measurement events for some applications is that time can be secretly shared because no classical time information is shared between the nodes.

[0058] Additionally, latency can be reduced since there is no waiting for a classical exchange of information to find coincidences or to otherwise establish the time-correlation and/or phase-correlation property and associated shared time and/or phase information of a photon that belongs to a quadruplet. Most practical systems will benefit from “starting” the accumulation of both lists at roughly the same time (as determined by a common reference). However, since coincidences in many practical real systems tend to occur at low rates (e g., milliseconds), the accuracy of this “start” time can be low. Importantly, in some configurations, simple (not precise) free running clocks can be used in each location. In some configurations, a common time reference and/or start time can be resolved simply by energizing, shuttering, or otherwise time-stamping the entangled source until ready to effectively “start” both lists at the time entangled photons start to arrive at both locations.

[0059] In some embodiments, the state dimension of the time basis is dependent on the clock resolution at each detector pair. The clocks can be running at nominally the same rate, to an accuracy that provides a desired resolution. If the time basis is a time between arrivals, delta- t, absolute time is only relevant to insure both detectors start their ordered list within a reasonable time window so that the subsequent post processing and correlations of the ordered lists don’t become unwieldly making absolute time irrelevant and clock accuracy requirements only relevant for short inter-arrival times.

[0060] One feature of the present teaching is that the amount of classical information shared between locations can vary as desired or required by a given application. In some embodiments, the classical information shared is the quantum metadata that is quantum data in a classical form associated with the quantum state information. Varying the amount of classical information shared can also be expressed as varying the level of classical communication isolation of the two locations. For example, the classical communication isolation can be complete, with no classical information shared, or the classical communication isolation can be partial with some classical information shared. As described above, by using coincidence of pairs of quadruplet, time-correlated photons, time and other quantum state information can be shared between locations without any need to send any classical information about the measured states. In various embodiments, different amounts of information about the measured quantum states, and associated lists of measured state information can be shared. Information about the measured quantum states that is not a value of one or more of the measured states be referred to as metadata as described herein.

[0061] FIG. 2B illustrates examples of measured event lists 230 that can be used for some embodiments of a system and method of sharing quantum information using time- correlated single photons of the present teaching. In some embodiments, a detected signal list 232, 234 of all measured photons at a detector as a function of time is generated. The detected signal list 232, 234 can be generated, for example, using the measurements from any one of the detectors 212, 214, 216, 218 as described in connection with FIG. 2A. The lists can also include measured data of events that are not associated with a time correlated photon, such as background count measurements. While in general, there is no discernable difference between measured events from correlated and background photons and/or detector dark counts, the lists 232, 234 illustrate time-correlated photons, e.g., event 236 of list 232 and event 238 of list 234 as a dotted line for clarity. Other measured background events from, e.g., background photons and dark counts, are shown with a solid line 240.

[0062] Systems using time-correlated photons look for coincidences in time at two different detectors. The background events align in time at different detectors only by chance. For uniform background arrivals with a known rate, it is possible to calculate the probability that these background events align in time. To the extent a reference time exists between nodes and flight and detection time latency from source to detector are taken into account, the arrival time of time correlated photon events 236, 238 in the two lists 232, 234 is the same. Regardless of relative time, time correlated photon arrival events occur with exactly the same time difference (within measurement error) between events if the two clocks run at the same rate. As such, by sliding and comparing the two lists as a function of time, represented by arrow 242, relative time between the two detectors can be determined. By sliding, we mean comparing the two lists at each of a series of different time shifts between the two lists. By comparing, we mean adding the number of matches per relative time position of the shift. So together by sliding and comparing, we are referring to the ability to generate a cross-correlation of the two lists.

[0063] A peak, with nominally the value of all the time-correlated photons (six in the example) will result at the matched position caused by the sliding, and be lower at other relative time position. Performing the sliding and counting matches method at various positions can provide a cross-correlation of the two lists 232, 234. As understood by those skilled in the art, cross-correlation can determine a similarity between two data sets, or two lists of events.

[0064] In some methods, coincidence event lists 244, 246 are generated. These lists may be generated, for example, from the output of the coincidence detectors 220, 222 described in connection with FIG. 2A. In some methods, coincidence lists 244, 246 can be generated by cross correlating and then producing a list of the times of matched events associated with the peak of the correlation. In some methods, only coincidence events from the detector 220 are listed as a function of time. If both a reference time and a clock rate of the two coincidence detectors 220, 222 are synchronized, each list is the same and represents shared information. This method has some advantages over methods that use background counts in the shared lists because the lists are reduced to contain only coincidence events, which in many practical systems is several orders of magnitude less than all events. As such, the size of a message containing the list is smaller and/or the amount of data to be processed during analysis of a list is less.

[0065] In methods where the reference time and/or clock rate synchronization is unknown, these lists can be shared, and a slide and compare operation, which is represented by

15 arrow 252, can be performed on the coincidence event lists 244, 246 to provide information to synchronize clocks in the two locations. See, for example, U.S. Patent No. 11,614,771 entitled Method for Synchronizing and Locking Clocks, which presents additional details, applications, systems, and methods for sharing quantum information using event lists.

[0066] In some methods, coincidence counts 254, 256 are generated. This kind of information about the measured events having no state value information is referred to herein as quantum metadata because this type of metadata is related to quantum state information, but does not contain any actual measured quantum state information. This quantum related metadata can be a number of the coincidence counts in a set time window generated at the output of the coincidence detectors 220, 222, which was described in connection with FIG. 2A. In this case, number 6 shown as 254, and number 6 shown as 256 are generated. These numbers are compared and determined to be equal, which provides a high likelihood that the coincidence events are not in error, for example an error caused by the loss of one or more photons, and the shared information about the coincidences is good information. As such, one feature of the present teaching is that the sharing of a number that has no meaning outside the two systems that are sharing that number, can be used to improve the fidelity of the shared information between the two systems while maintaining privacy.

[0067] FIG. 2C illustrates a schematic diagram 260 of entangled photon sets 298, 299 used in embodiments of a system and method for sharing quantum information using time- correlated single photons of the present teaching. The diagram 260 illustrates an example for quadruplets (four) of entangled time-correlated photons, and shows just two sets 298, 299 of quadruplets for clarity. Typically, streams of many entangled photon sets are generated over time. In addition, more, or less, than four photons in a set of entangled photons can be used. [0068] One set 298 of entangled photons includes four photons 261, 261’, 261”, 261”’. The set 298 of four photons 261, 261’, 261”, 261’” is shown aligned vertically to suggest how they are time-correlated, that is they originate at a common time. The other set 299 of entangled photons includes four photons 262, 262’, 262”, 262”’. The other set 299 of four photons 262, 262’, 262”, 262’” is also shown aligned vertically to suggest how the photons 262, 262’, 262”, 262”’ are time-correlated, that is they originate at a common time. The common time for the two sets 298, 299 is different since they are generated at different times. It should be understood that background photons, while commonly present are not shown in the diagram 260 for clarity.

[0069] One feature of the present teaching is the recognition that the set 298 of four entangled photons 261, 261’, 261”, 261’” are all correlated in time and so one pair 263 of photons 261, 261’ of the set 298 of four entangled photons being correlated in time indicates that all four photons 261, 261’, 261”, 261’” of the set 298 of four entangled photons are entangled. This is an important feature that allows, for example, exploitation of the non-local and/or high precision features of the time correlation that crosses all four photons 261, 261’, 261”, 261’”. This is possible because sets 298, 299 of four entangled photons that are time correlated can be determined by coincidence determination of only two photons in the set. For example, coincidence of pair 263, and/or coincidence of pair 267, identify set 298. Likewise, coincidence of pair 265, and/or coincidence of pair 268, identify set 299. This identification then enables the exploitation of some or all of the entangled state information that is carried by the set 298, 299. That is, just determining that a pair is correlated photons indicates that all four photons are correlated. More generally, determining a subset of photons in an entangled set is correlated indicates another subset, or subsets, of the same set are correlated.

[0070] As such, some embodiments of a method of the present teaching determine a coincidence of the one pair 263 of photons of the set 298 of four entangled photons 261, 261’, 261”, 261’” and also detect at least one photon 264/261” that is not in the pair 263 of photons of the set 298 of four entangled photons 261, 261’, 261”, 261’”. The detection of the one photon 261” can be, for example, a simple indication that a detection event occurred. The indication may be a mark in a time bin associated with the detection of the photon 261”. The detection can be configured to generate additional state information about the photon 261”. For example, a detection event can include additional measured quantum state information carried by the detected photon, including a precision time of arrival, polarization, wavelength, phase and/or position of the detected photon. This additional state information can be realized, for example, if the quadruplet is hyper-entangled in multiple bases, and the detection event is made appropriately sensitive to the hyper-entangled bases.

[0071] By detecting a photon, we mean generally making a measurement of one or more of the quantum states being carried by that photon. An example of detecting is one or more of measuring a time of arrival of a single photon, measuring a polarization of a single photon, measuring a wavelength of a single photon and/or measuring a position of a single photon. Measuring single photons can be done using known single photon detectors, including various photo multiplier devices, avalanche photodiodes, Geiger mode detectors and other single photon detectors. Other state information can be determined in the measurement, for example using various optical analyzers before a single photon detector or detectors. Thus, detecting one or more properties of a single photon can require use of more than one single photon detector. Importantly, a detection of a single photon is a singular measurement event and all properties that are derived from that measurement event are tagged to that particular photon. In this way, a so-called detection of a photon can produce multiple state values. [0072] The method continues by determining that the at least one photon 264 from the other pair 267 of the set of four entangled photons 261, 261 ’, 261”, 261”’ is entangled using the coincidence of the one pair 263 of photons of the set 298 of four entangled photons. Thus, the entanglement of the set 298 of four entangled photons is identified from the coincidence of the one pair 263 of photons of the set of four entangled photons.

[0073] Stated another way, one aspect of the present teaching is the highly useful concept that knowledge of entanglement of all four photons can be determined from the detection of only two. This capability serves to separate, or make independent, an identification of an entangled set of photons, and other measures of quantum state information of at least some other photons in the set of entangled photons. For example, it is possible that some photons in an entangled set are used to identify the entangled set, and other photons are used to derive or exploit other quantum information of that entangled set. That is, once an entangled state is identified by determining coincidence of pair 263, it is possible to exploit entangled quantum state information that is carried by, for example, the single photon 264 after its measurement or, more generally, any other subset of photons in the set 298.

[0074] The identification method can be used, for example, in a system where the determination of the coincidence of pair 263 is used to herald the entangled photon 264. The identification can be used, for example, to synchronize a clock that is part of or connected to a system that is determining the coincidence of pair 263 and another clock that is part of or connected to a system that is detecting the photon 264. Numerous synchronization configurations and performance parameters can utilize this method.

[0075] The identification method can be used in real time or essentially real time, assuming sufficient attention is given to delays and time-synchronization for both the coincidence determination and the photon measurement/detection. The identification method can also be used in non-real time systems. In non-real-time systems, measurements are made at one time or over different times, and then subsequently analyzed and/or compared. Timecorrelation identification and entangled state information derived from the combination of the coincidence determination and the detected photon 264 are determined and/or exploited at some point after one or both of the measurements are completed. This can be done if the information about the coincidence determination and/or the detection events are kept in lists that represent the measurement events or contain the measurement information that is pertinent to identification. The lists are then subsequently used for analysis and/or comparison to identify entanglement and/or to determine quantum state information.

[0076] In some methods, the pair 263 is sent to one location, measured and processed to determine coincidence in one location and the other photons in the set 298, including at least the detected photon 264, are sent to a different location for the detection. In these cases, the lists containing measured event information that are generated in the two locations can be shared or exchanged, e.g. over a network or other classical communication link.

[0077] In general, various lists described in connection with the present teaching, such as, for example, the lists described in connection with FIG. 2B, will contain information about numerous entangled set elements as well as background counts and measurements of photons that are not part of entangled sets.

[0078] Key features of the generated lists can be understood by distilling down to just two entangled set elements shown in the diagram 260 of FIG. 2C. The diagram 260 shows the other set 299 of photons 262, 262’, 262”, 262’” that include a pair 265 of photons 262, 262’ and also a single photon 266, photon 262’, of the other pair 268 of photons 262”, 262’”.

[0079] Some embodiments of the method of the present teaching generate a set 298 of entangled photons 261, 261’, 261”, 261”’, and then determine a coincidence of one pair 263 of photons 261, 261’, and detect one photon 264 of the other pair 267. It is therefore determined by the coincidence event that the detected one photon 264 of the other pair 267 is entangled in the set 298. As such, the determination of coincidence of pair 263, which can potentially be completely independent of the detection event of detected photon 264, identifies that entanglement status. This same process is repeated for the other set 299 of photons 262, 262’, 262”, 262”’. The set 299 is generated, a coincidence of one pair 265 of photons 262, 262’ is determined, and a measurement of a photon 266 of the other pair 268 of the set of entangled photons 262, 262’, 262”, 262’” is performed.

[0080] After generation and measurement of both sets 298 and 299 of photons, based on the determined coincidences, a first list of state values corresponding to both the identified set 298 of four entangled photons 261, 261’, 261”, 261’” and also the identified other set 299 of four entangled photons 262, 262’, 262”, 262’” is generated. In this simple two-set example, the list can include, for example, two entries that are a determined coincidence time for each set 298, 299. This list can be presented or stored in numerous ways. The list can be marks in regularly spaced time bins that indicate the time-bin corresponding to when the coincidence determination is made. The list can also, or in addition, be presented as timestamps of the coincidence determinations. The list can also, or in addition, include additional state values, such as the difference in arrival time between the two determined coincidences, a polarization value, a wavelength value, a spatial position, or a phase value associated the pairs 263, 265. Lists can also be generated to include measured values of some or all of the individual photons 261, 261’, 261”, 262, 262’, 262’ ’ as dictated by the application. The particular content of a list can be based on the application need as well as the specific system and method used for the measurements, detections and coincidence determinations.

[0081] One feature of the present teaching is that two, potentially widely geographically separated and/or classically isolated, coincidence determinations of different pairs in a set of entangled photons provide an effectively latency free, or non-local, sharing of quantum information carried by (or contained within) the entangled set. Thus, a determined coincidence of the other pair 267 of photons 261”, 261’” of the set 298 of four entangled photons 261, 261’, 261”, 261”’ identifies the entanglement of the set 298 of four entangled photons 261, 261’, 261”, 261”’ and a determined coincidence of the other pair 268 of photons 262”, 262’” of the other set 299 of four entangled photons 262, 262’, 262”, 262’” identifies the entanglement of the other set 299 of four entangled photons 262, 262’, 262”, 262’”. A second list of state values corresponding to both the identified set 298 of four entangled photons 261, 261’, 261”, 261’” and also the identified other set 299 of four entangled photons 262, 262’, 262”, 262’” is generated that is based on the determined coincidence of the other pairs 267, 268.

[0082] This second list is based on measurements of different pairs than the first list, however, the first list of state values and the second list of state values are correlated. That is, a first list is generated by measurements of pair 263 of photons 261, 261’ of one set 298 of entangled photons 261, 261’, 261”, 261’” and by measurements of pair 265 of photons 262,

262’ of the other set 299 of entangled photons 262, 262’, 262”, 262’”. The second list is generated by measurements and coincidence determinations of the other pair 267 of photons 261”, 261’” of one set 298 of entangled photons 261, 261’, 261”, 261’” and by measurements and coincidence determinations of the other pair 268 of photons 262”, 262”’ of the other set 299 of entangled photons 262, 262’, 262”, 262’”.

[0083] In some embodiments, these measurements of the detections and coincidence determinations that contribute to the first and second lists are performed in one localized node and/or with one clock providing timing. In other embodiments, these measurements of the detections and determinations are performed in more than one node and/or with more than one clock providing timing.

[0084] One feature of the present teaching is that the hardware and processing needed to determine coincidence and/or measure state information of photons can be constructed using relatively simple and low-cost components. FIG. 2D illustrates an embodiment of a receiver 270 for measuring a pair from time-correlated quadruplets of the present teaching. The receiver 270 can be used, for example, as an implementation of detectors 212, 214 and coincidence detector 220, and/or an implementation of detectors 216, 218 and coincidence detector 222 as described in connection with FIG. 2A. Detectors 272, 274 generate an electrical signal in response to receipt of time-correlated photons, and may also generate electrical signals in response to background. The detectors can be configured so the electrical signal is high when a photon is detected. The outputs of detectors 272, 274 are input to two inputs of a logical AND gate 276. Time-correlated photons will cause the AND gate 276 to generate a high signal because both inputs are high. A clock 278 in the receiver generates a clock waveform 280 with a cycle time T cycle. The clock produces time stamps 282 each cycle. A controller 284 can move a stamp 286 to a buffer 288 when the output of the AND gate 276 is high to store a list of timestamps of coincidences The controller 284 can determine a difference 290 between time stamps at two high-values from the output of the AND gate 276 to the buffer 288 and a Delta-T timestamp list is generated.

[0085] Some embodiments of the time-correlated photon identification system of the present teaching use an AND logic gate and processing to determine shared quantum information from time-correlated quadruplets. FIG. 3A illustrates an embodiment of a system 300 for sharing quantum information using time-correlated single photons generated by a SPDC source of the present teaching. The source 302, generates four streams of photons that include at least some time-correlated photons at outputs labeled a 304, b 310, c 306 and d 308. The source 302 can be, for example, the source 100 described in connection with FIG. 1. These outputs are each optically connected to detectors 312, 314, 316, 318. One pair of detectors 312, 314 has outputs connected to a processor 320 and an AND gate 322. Another pair of detectors 316, 318 has outputs connected to a processor 324 and an AND gate 326. The outputs a 304 and c 306 can be optically connected to a node 328 that is physically distinct from a node 330 connected to outputs d 308 and b 310. As described in connection with FIG. 1, a feature of the source 302, is that a coincidence that can be found through the AND operation of the gates 322, 326 in either node 328, 330 has a very high likelihood of indicating a correlated quadruplet of four photons emerging from a 304, c 306 d 308 and b 310.

[0086] In some embodiments a BBO crystal 328 is energized with a pump laser beam 330 that is reflected back at the BBO crystal 328 by a mirror 332. The resulting output along directions of a, b, c, and d includes various singles, doubles (pairs) and quadruplets that are time correlated photons. The allowed states of this system are as follows: 1) random single photons at arbitrary times at a, b, d, and c; 2) two-way coincidences at a and b only; 3) two-way coincidences at d and c only; and 4) four-way coincidences at a, b, d and c. Excluded states of this system are as follows: 1) two-way coincidence at a and c without a coincidence at d and b; 2) two-way coincidence at b and d without a coincidence at a and c; 3) three-way coincidence at a, c and d without a coincidence at b; 4) three-way coincidence at a, c and b without a coincidence at d; 5) three-way coincidence at d, b and a without a coincidence at c; and 6) three- way coincidence at d, b and c without a coincidence at a.

[0087] In this embodiment of the system 300, by carefully choosing the pairings of a, c, d, and b from the source 302, we can guarantee with a high likelihood that if a and c see a coincidence, d and b will see a coincidence.

[0088] FIG. 3B illustrates a table of cases for an event list associated with an embodiment of the system for sharing quantum information using time-correlated single photons of FIG. 3A. In general, an event is registered either for a random or a time-correlated (marked coincidence) photon to be registered at each of outputs a, b, c and d. Allowed cases are random events at a, b, c and d, coincidences at a and b (entangle pairs), coincidences at c and d (entangle pairs) and coincidences at a, b, c and d (quadruplet). The other cases are not allowed.

[0089] FIG. 3C illustrates a table 370 of lost photons and false coincidences for an embodiment of the system for sharing quantum information using time-correlated single photons of FIG. 3A. This table 370 columns refers to detectors described in connection with FIG. 3A. It should be understood that the more likely “error” scenario for a quadruplet is lost photons. That is, although a quadruplet is present at the source outputs a, b, c and d, in the quantum channel to nodes 328, 330, one or more of the entangled photons are lost in the channel on the way to the detector or as a result of imperfections in the detector itself. If detector DI A 312 “looses” a photon, but DIB 316 and D2B 318 do not, the node 330 will assume that it has time-correlated photons and will add the information detected to its ordered list, but node 328 will not, and the ordered lists will no longer match up. But if D2A 314 loses a photon, and DIB 316 loses a photon, neither node 328 or node 330 will add to their ordered list, so no errors are incurred (a detected error) although a time-correlated event is lost. The table 370 outlines when an undetectable error would occur, which is 6/16 possible combinations.

[0090] There are various ways to compensate for lost time-correlated events. For example, various methods for compensating for lost time-correlated events include using a classical channel for error detection and/or correction. However, unlike a two-way entangled situation, a classical channel can be used to detect and/or correct these errors with a minimum of information exchange (low bandwidth) for time-correlated quadruplets.

[0091] In one method of error correction and/or detection, nodes 328, 330 keep a running count of coincidences and periodically share their numbers through a classical channel. This is a type of parity error checking and correction but does not require the use of additional signal. In one method, the numbers do not match, the nodes 328, 330 know photons have been missed.

The nodes 328, 330 know that the difference between counts equals the number of missed photons, and the detector with the lower number is the one with missing counts. One bandwidthefficient method to manage this would be to exchange counts at a rate approximately equal to the expected loss rate making the probability of a single lost photon during a counting interval equal to 0.5. If the counts match, the lists match. If they do not, at least one missing photon case is identified.

[0092] If there is a missing photon, both nodes 328, 330 could purge their lists for the interval since the last matching count exchange. Alternatively, nodes 328, 330 could exchange their counts for half the list, and see if the counters match. If the counters match, then each node tries for three-quarters of the list. If the counters do not match, then each node tries for one- quarter of the list. Successively cutting the remaining list in half, or doubling it, until the counts match, allows identification of additional time-correlated photons that might otherwise be discarded.

[0093] There are other ways to detect and correct errors, with a low information rate classical exchange. For example, the nodes 328, 330 could share polarization values, but keep time of arrival as a shared secret. This is highly valuable given the large state dimension that can be realized with time. For example, time can be measured to very high accuracy, for example, picosecond or higher. As such, a value with many digits of precision can be shared for each measured entangled set as compared with polarization, which may have only two bits of precision. If polarization values do not match, the most likely reason would be a lost photon as described above. Because both these bases (polarization and time) are carried by the same entangled photon set, low-bit value (only two bits of precision) polarization can be used to improve the accuracy of the large number of bits contained in shared time values.

[0094] As another example of a method of detecting and correcting errors, nodes 328 and 330 can share their list of coincidence event time stamps or combs. Any missing coincidences are discarded. As another example of a method of detecting and correcting errors, quantum metadata that is wavefunction data that indicates particular time windows where entangled photons are not generated is used to discard any measured state values that are found in that window.

[0095] A local coincidence detector can very accurately measure coincidences in short time windows can be inexpensively constructed using the present teachings. The resultant measurement accuracy reduces the error rate due to false entanglement. The more likely errors in time correlated quadruplets are related to lost photons errors. If losses due to lost photons are low, it is possible to build a system with no classical channel between nodes 328, 330. If losses due to lost photons are higher, it is possible build error detection and correction schemes that share information between processors 320, 324 in nodes 328, 330 that require only a very low information transfer rate, as compared, for example, to systems that exchange information using pairs of time correlated photons only.

[0096] The probability of error caused by singles arriving simultaneously (false coincidences) at DI A 312 and D2A 314 or DIB 316 and D2B 318 is limited by the speed of the local coincidence detector, which effectively determines the equivalent resolution of time stamps or size of time bins. The exact formulas have been derived for pairs, see, for example U.S. Patent Number 11,614,771, entitled “Method for Synchronizing and Locking Clocks”, which is assigned to the present assignee and incorporated herein by reference. Low cost, high-speed AND logic gates which can be used to detect coincidence are widely available. For example, the Fairchild Semiconductor 74VHCT08A is specified to run at 5 ns and costs $0.10. With a 5 ns window, the expected value of a false coincidences per second (false entanglement) in a system generating 10,000 singles per second is given by:

10,000 2.5 * IO ^-5 .

[0097] When two detectors are co-located, a simple logical AND condition can determine coincidences with high time resolution. When the two detectors are remote from each other, we can exchange a quantum state comb over a classical channel to find coincidences. A quantum state comb (hereinafter “comb”) is an ordered list of measurement events. That is, a quantum state comb is a list of measured states in the order they arrive at a measurement node and/or a particular detector or group of detectors in the measurement node. A quantum state comb can also be an ordered list of measured events from different spatial positions. Also, a quantum state comb can be an ordered list of measured events from different polarizations or from different colors. Also, quantum state combs can be a combination of measured events that include any combination of the above and any other type measured events. The quantum state comb time can be measured from various bases, such as a local clock, which can be synchronized in a relative and/or absolute basis to a non-local clock. The local clock can be a free running clock that is synchronized using shared entanglement via methods described herein. It should be understood that a quantum state comb includes more than one value per measured state. The value can be, for example, polarization, arrival time, frequency/color and/or spatial position. This is the case, for example, if an entangled state is a hyper-entangled state, where a single photon of a pair or set is entangled in more than one way (dimension or basis). In some embodiments, different members of a comb have different values. That is, a comb can include more than one type of entangled state where the more than one types are not entangled with each other. This could be the case, for example, if quantum states from two different sources generating entangled states were multiplexed. This could be done, for example, to increase the rate of entangled pairs being generated.

[0098] That process requires exchanging information that includes singles and coincidences then sliding the combs past each other to find the maximum number of overlaps (e.g. cross correlation). Since many practical entanglement sources produce singles at a rate that is three or four orders of magnitude greater than the coincidence rate, a large amount of information must be exchanged and processed, most of which consists of background noise in the form of singles.

[0099] For example, if a given source has a singles rate of five thousand per second, and a coincidence rate of ten photons per second, then five-thousand-ten events must be exchanged over the channel per second of data collection. Subsequent processing involves sliding the two combs past each other. That process requires a number of comparison steps that is equal to the l/(time resolution) X (2 x the clock uncertainty between the two detectors). As an example, if the time resolution was 10 ns, and the clock uncertainty was 100 microseconds, the step count would be 1/10 ns X 2 X 100 ms = 20 Million comparison steps. By contrast, if only coincidence information is exchanged, the step count would be eleven.

[00100] FIG. 4 illustrates an embodiment of a system 400 for sharing quantum information within a single node 415 using time-correlated quadruplets of the present teaching. The source 402, generates four streams of photons that include at least some time-correlated photons at four outputs that are optically coupled to four detectors 404, 406, 408, 410. The four detectors 404, 406, 408, 410 each generate an electrical signal at an output in response to receiving a photon generated by the source 402. The outputs of each of the detectors 404, 406, 408, 410 are connected to a processor 412. In this embodiment, the detectors 404, 406, 408, 410 and the processor 412 are physically positioned in a node 415. The present teaching is not limited to a particular type of node 415, but generally the node is configured to support localized, low-latency, information exchange and control over positions and time-of flight within the node 415. The source 402 can be, for example, the source 100 described in connection with FIG. 1, but can be any photon source that generates time-correlated photons. Each of the four detectors 404, 406, 408, 410 is connected to one of the four outputs from directions a 414, b 416, c 418 and d 420. [00101] In this embodiment, the table 350 described in connection with FIG. 3B lists allowed conditions for event detections at the four detectors 404, 406, 408, 410. A feature of this system 400 configuration, with all detectors co-located, is that it is easy to provide basic synchronization between the four detectors 404, 406, 408, 410. As such, the fine-grain, high resolution time correlation of the quadruplets can be easily exploited, because the local clocks are classically well synchronized. The processor 412 can include one or more logical AND gates or software to provide the logical functions. The AND gates produce a “high” signal when both input signals at the input are “high” and produces a “low” signal otherwise. Thus, coincident detections at any pair of detectors produce a “high” signal at both detectors’ outputs. When these outputs are connected to two inputs of an AND gate a “high” output is produced at that AND gate, which is synonymous with the detection.

[00102] For example, two detectors 404, 406 can be connected to an AND gate in processor 412 and the other two detectors 408, 410 connected to a different AND gate. When the outputs of the two AND gates are both high because photons are present at all four detectors 404, 406, 408, 410, a time-correlated quadruplet is identified. This assumes equal time-of-flight from source to detectors and through AND gate outputs. It is understood that unequal times of flight can be addressed in various known ways.

[00103] We note that if the outputs of the two AND gates are provided to another AND gate, when that third AND gate is high, it correctly identifies the presence of a time-correlated quadruplet. This is true regardless of which pairs of detectors 404, 406, 408, 410 are connected to the AND gates. By putting outputs from detectors coupled to a front side (a or b) and a backside (d or c) into the same AND gate, it reduces the number of AND gate high counts, because the probability of singles appearing at the same time from the front and back directions is low. This can reduce the number of false identifications of time-correlated quadruplets based on a single AND gate connected to just two detectors being high. In some embodiments, this eliminates the need for a third AND gate to identify a time correlated quadruplet.

[00104] In this configuration, quantum metadata that is wavefunction data that indicates particular time windows where entangled photons are not generated can be used to discard any measured state values that are found in that window. This can be realized by having a metadata collector (not shown) that generates a “high” signal during time windows were single photons are generated, and a “low” signal otherwise. Taking this metadata signal and putting it into an AND gate into processor 412 with any or all of the inputs from detectors 404, 406, 408, 410 can prevent false positives.

[00105] FIG. 5 illustrates an embodiment of a system 500 for sharing quantum information of the present teaching that includes an interferometric path-difference measurement. The sharing of quantum information can include, for example, determining photon coincidences and determining information about a sample through interferometric measurements. In some embodiments, this interferometric measurement is a HOM-dip measurement. One pair of photons from a quadruplet emitted by a source 502 is measured using two detectors 504, 506 in an interferometer 508 configuration and the other pair of photons are also detected and one or more of those detected signals are used for processing that identifies the quadruplet. Identification of the quadruplet effectively heralds an interferometric measurement event as a pair. Equal paths from the source 502 through the interferometer 508 taken by the photons of a correlated pair result in detection at only one of the two detectors at the interferometer output. This may be referred to as a coincidence null position. The coincidences as a function of path length differences between the pair follow a HOM curve as illustrated, for example, in C.K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of Subpicosecond Time Intervals between Two Photons by Interference,” Phys. Rev. Lett., vol. 59, no. 18, p. 2044, 1987. The identification of the quadruplet in the system measurement when configured to identify a HOM dip position, unlike prior art HOM systems, can mean there is no need to dither path lengths around a HOM dip position to better pinpoint that position. Quadruplet identification can also reduce the number of measurements taken to “find” the dip. In addition, the number of accidental coincidences can be substantially reduced, thus supporting operations in high background noise.

[00106] In this embodiment of measurement system 500, light coupled from direction a is coupled to a detector 510. Light coupled from direction d is coupled to a detector 512. Light from direction c is coupled to a path and directed by a mirror 514 to a beam splitter 516. Light from direction b is coupled to a path and interacts with a sample 518 and is directed to the beam splitter 516. The light from the two paths interferes on the beam splitter and produces output along two paths, one output path being coupled to a detector 504, and the other is coupled to a detector 506. Single photon interference causes an interference pattern in the probability density of the photons arriving at the two detectors 504, 506 based on the path length difference for light from direction c and b at the beam splitter 516. Thus, the pattern of coincidence of photon pairs measured at the detectors 504, 506 provides path difference information of the flight of the two photons. This in turn can provide information about, e.g. refractive index, thickness, position, and other features of the sample 518.

[00107] The outputs of the detectors 504, 506, 510, 512 are processed in a measurement processor 519. To determine the pattern of coincidence as a function of time and/or path difference, the output of detector 504 and detector 506 are input to an AND gate 520 in the processor 519. Also, the output of detector 504 and detector 510 are input to AND gate 522 and the output of detector 506 and detector 512 are input to AND gate 524. The AND gates produce a “high” signal when both input signals at the input are “high” and produces a “low” signal otherwise. Thus, coincident detections at any pair of detectors connected to two inputs of an AND gate produce a “high” output at that AND gate synonymous with the detection. The outputs of the AND gates 520, 522, 524 are provided to a coincidence processor 556. The coincidence processor 556 can process the outputs from the AND gates 520, 522, 524 in numerous ways. For example, the “high” signal from one or both of AND gates 522, 524 can be used as a trigger to look for a coincidence-indicating “high” signal from AND gate 520. An absence of “high” signal from AND gate 520 would indicate the interferometer is at or near a “dip” position. The number of “highs” from one or both of AND gates 522, 524 that coincide with “highs” from AND gate 520 as a function of path length differences between c and b can produce more details on HOM interference information that corresponds to phase information of the sample 518. In some embodiments, the various elements of the receive side of the HOM system are enclosed in a node 528.

[00108] As understood by those skilled in the art, aspects of the identification of entangled quantum information from correlated photons is not necessarily restricted to the use of time- correlated quadruplets, and other numbers of photons in a set can be used. For example, identification of a pair of correlated photons can be done using only one additional correlated photon in a set, i.e. a triplet. In this case, coincidence of the photon in the set that does not pass through the interferometer with detection of a photon in one or both of the detectors at an output of the interferometer can be used to identify the entangled pair whose path length difference are being measured by interferometer using only three time-correlated photons. [00109] As such, some embodiments of the interferometric measurement system and method of the present teaching advantage of the time-correlations of sets of only three photons to provide “heralding” of the two-photon interferometer output. In these embodiments, and referring to FIG. 5, the source 502 needs only to produce three entangled photons at three outputs, for example, a, b and c. Two photons enter the interferometer 508 and are detected by detectors 504, 506, and an additional photon is measured by detector 510. Coincidences between detected photons from detectors 504, 506 provide information on the path difference between photons following paths b, c from source 502 to beam splitter 516. Coincidences between either of detector pairs 510, 504 or detector pairs 510, 506 indicate that the presence or absence of coincidences between pair 504, 506 are a direct measure of a path difference from the source 502 to the beam splitter 516. For example, a presence of a coincidence at either of detector pairs 510, 504 or detector pairs 510, 506 with the absence of a coincidence between pair 504, 506 indicates that the path difference is zero.

[00110] As understood by those skilled in the art, HOM interference information can be used to determine properties of the sample 518 as, for example, mirror 514 is adjusted. That is, the path length difference can be adjusted by appropriate movement of mirror 514 to produce a HOM interference pattern as a function of different path lengths for signals passing through the interferometer from paths c and d. In some embodiments, multiple measurements can be taken for each relative path length position to improve the fidelity of the “dip” identification, but in some embodiments, a single measurement at a particular position is sufficient. In general, by using quadruplets, or triplets, of time-correlated photons to help identify coincidences of some of the pairs of photons in the quadruplet, a single interferometer measurement, or an interferometric scan, can be produced in a much shorter time than a system that relies only on pairs of photons that are not part of a quadruplet.

[00111] Said another way, systems using time-correlated quadruplets of the present teaching make it possible to tell the difference between a HOM dip and a quiet channel. Prior art systems cannot do this using a spontaneous entangled photon generator. In these prior art systems, the only way is to know that there is an entangled pair hitting the beam splitter. Thus, in systems of the present teaching according to this embodiment, when no signal is observed at the interferometer outputs while a coincidence is detected from another pair, then the zero is known as a HOM dip.

[00112] Furthermore, known interferometric measurement systems that use entangled single photons need to average a measurement of a single path difference in the interferometer to include more than one pair of photons. Typically, averaging times per path difference measurement are durations of seconds, or even minutes, for cases where the entangled photons are generated with rates of between 10-10,000 entangled photon pairs per second. For example, these systems can require lO’s-lOOO’s of entangled photon pairs to make a single path difference measurement. Interferometric path difference measurement systems using time-correlated photon identification of the present teaching can make a path difference measurement with high confidence using just a single set of entangled photons.

[00113] One feature of the system and method of the present teaching is that is can be relatively robust to lost photons in the time-correlated quadruplets. That is, if one or more photons of the set is not measured for some reason it is referred to as lost. For example, if a photon that is part of the pair detection (coincidence) is lost, we only lose a detection of the null opportunity for that photon set, and need to wait for the next set to arrive for a null identification. As such, the loss of this photon does not create an error, it merely increases the wait time of the identification of the null. The wait time depends on the generation rate of entangled sets. If a photon of the pair that is in the interferometer is lost, then a null will not be detected. Then, a coincidence is measured, and so a null is queried but not seen. This is a false non-null. This could lead to unwanted adjustment, but it also is not necessarily a serious error. This could mean in some systems that more than one successful measurement needs to be taken to validate a null. Accounting for possible false nulls slows down the process of null identification, but can be managed with known techniques.

[00114] Generally, systems and methods of the present teaching lead to one variable associated with the determination of a dip being effectively removed by the use of pairs from quadruplets, and this leads to improved performance. The above description of the embodiment of FIG. 5 is focused on the use of the quadruplet identification to find a HOM dip by having known pairs and so deterministically establishing the absence of the coincidence. However, as understood by those skilled in the art, the independent confirmation of a pair, akin to the commonly used heralding for single photon systems, can be applied in numerous ways.

[00115] For example, identification of the quadruplet or triplet which heralds an entangled pair in the interferometer can be used to stabilize the system, to improve the signal to noise of the system, and/or to reduce the latency of interferometric measurements and associated position, thickness, refractive index, birefringence and other sensing information derived from the measurements. It is important to note that this identification coincidence is independent from the interferometric measurement coincidence, and does not impact or diminish the fidelity of that measurement in any way. The independent pair identification can be applied at all path-length- difference positions of the HOM curve, or interferometric measurement curve. As will be understood by those skilled in the art, although a two-path reflective interferometer configuration is shown as an example, numerous known interferometer configurations can be used. For example, other two-arm interferometric configurations, single arm configurations, including time-slot and polarization-based single arm configurations, and counterpropagating configurations can be implemented. For example, Mach-Zehnder, Michelson, Fabry-Perot, Fizeau, Twyman-Green, Gires-Tournois, Sagnac types of interferometers can be implemented. In addition, sample properties can be determined using reflection and/or transmissive configurations in one or both paths that converge on the beam splitter (or other interferometric combiner) of the interferometer.

[00116] Many sources of quadruplet, triplet or dual entanglement also emit single uncorrelated photons at high rates that may be two or more orders of magnitude greater than entangled photons. Other sources of uncorrelated signals that manifest as single counts can be noise sources such as light in a room, or natural light from the sun and other background photon sources. It is advantageous in many applications to use low cost sources of entanglement that emit large quantities of singles. It is advantageous in many applications to operate outdoors in daylight or in strong artificial light. It is also advantageous in many applications to operate in an environment where a malicious 3 ^rd party may produce noise photons.

[00117] The single uncorrelated photons from many of the common background sources occur at random intervals. If these random intervals overlap within the time resolution of detection hardware, AND gates or other coincidence detecting processors, they can be miscategorized as entangled photons. Since these uncorrelated photons are generated at statistically independent times, the probability of this miscategorization is the product of the probability of an uncorrelated photon arriving within a given time resolution raised to the power of the number of photons per set, which also corresponds in some embodiments to the number of detectors. Thus, for pairs entanglement, the error is proportional to the probability of an uncorrelated photon arriving within the time resolution squared. For triplet entanglement, the error is proportional to the probability of an uncorrelated photon arriving within the time resolution cubed. For four-way or quadruplets entanglement the error is proportional to the probability of an uncorrelated photon arriving within the time resolution to the fourth power. As such, interferometric measurement systems of the present teaching reduce the probability of errors in identification of a valid measurement point exponentially with the number of additional photons in the entangled set that are determined coincident with the measurement point photons.

[00118] As a numerical example, the probability of accidental coincidence in a microsecond window for a pair of detectors with random arrivals of 100,000 background photons per second at each detector is 1%. Three accidental coincidences probability is 0.1%, and fourway accidental probability is 0.01%.

Equivalents

[00119] While the Applicant’s teaching is described in conjunction with various embodiments, it is not intended that the applicant’s teaching be limited to such embodiments. On the contrary, the Applicant’s teaching encompasses various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art, which may be made therein without departing from the spirit and scope of the teaching.