Method and apparatus for determining offset for time synchronization in communication network

Abstract

A method of determining an offset between a first time reference and a second time reference is disclosed. The method comprises: obtaining (102) information relating to a detection time of a first photon of a first pair of photons at a first node and a detection time of a second photon of the first pair of photons at a second node; obtaining (104) information relating to a detection time of a first photon of a second pair of photons at the first node and a detection time of a third photon at the first node; and determining (106) an offset between a first time reference at the first node and a second time reference at the second node based on the obtained information. An apparatus, computer program and computer program product for determining an offset between a first temporal reference and a second temporal reference are disclosed.

Description

Technical Field

[0001] Examples of the present disclosure relate to methods and apparatuses for determining an offset for time synchronization in a communication network. Background Art

[0002] Telecommunication networks use highly accurate clocks in order to, for example, timestamp events and avoid bit slips during communication. Most relevant synchronization requirements for telecommunication networks are defined by the 3GPP standardization body and then delivered by a variety of techniques: Global Navigation Satellite System (GNSS), Over-the-Air Synchronization (OAS), Frequency over Transport, Transmission Time / Phase, and Clocks. GNSS consists of a set of satellites hosting atomic clocks. Signals from the atomic clocks are sent towards the Earth and received by GNSS receivers. In a 5G telecommunication network, the reference clock from GNSS is used by a digital unit that distributes the clock to radio units. The radio units can in turn use over-the-air synchronization to synchronize another radio unit. The digital unit also distributes the clock over the transport network using a timing protocol such as the Precision Time Protocol (PTP). A backup system is implemented via a PTP network that is fed by a geographically redundant Telecommunication Grand Master (T-GM) and distributes timing on the same physically redundant topology used for user traffic. The T-GM in turn receives signals from GNSS [1]. However, it is well known that GNSS can be spoofed or malfunction. For GNSS, the origin of the signal cannot be verified beyond doubt.

[0003] Time synchronization in current communication infrastructures is required for synchronizing communication time slots and timestamping events. For 5G, it is required to prevent interference in Time Division Duplex (TDD) communication. A typical target requirement is about 1 microsecond relative to an absolute reference. Time synchronization is also required in 5G for combining radio signals in carrier aggregation and dual connectivity. The target requirement is a 3 microsecond Time Alignment Error (TAE), and even more stringent requirements (260 - 65 nanoseconds) are applied for co-located antennas. Future communication infrastructures are expected to require even more stringent timing requirements in the nanosecond range.

[0004] Fiber Time Transfer (TTOF) enables the synchronization of remote clocks connected by optical fibers. An amplitude-modulated continuous wave laser, a mode-locked laser, or frequency combs generate synchronization signals. The Two-Way Time Transfer over Fiber (TWTTOF) scheme allows compensating for propagation length fluctuations in the optical fiber. Compared to GNSS, TWTTOF using dispersion-compensating fibers achieves lower time deviations (sub-picoseconds). However, time precision can be an issue for TWTTOF [1].

[0005] Security is a major concern for the implementation of TTOF. Quantum TWTTOF provides a solution and has been demonstrated using a frequency-entangled photon source based on spontaneous parametric down-conversion (SPDC) [2]. Single-photon detectors (e.g., superconducting nanowire single-photon detectors (SNSPD)) register single photons, and then an event timer (ET) correlates the detection events. Bell inequality tests can ensure the security of the process by verifying the entanglement of the registered photons, thus authenticating the source of the photons.

[0006] Photon statistics can be used to classify different states of light. If we consider the average photon number (i.e., the average number of photons in the mode) and the probability distribution of this photon number, we obtain three types of distributions: sub-Poissonian, Poissonian, and super-Poissonian. A special type of sub-Poissonian light exhibits a Dirac delta distribution, which means that a source of this light with an average photon number of 1 will only produce single-photon states. In contrast, a source of light with a different distribution and an average photon number of 1 will have a probability that the source emits 0, 1, 2, 3 photons or more photons per emission event and the probability is greater than 0.

[0007] Reference [2] is an example of a method for quantum time synchronization using a highly attenuated laser and a crystal (i.e., an SPCD source). For this type of source, there is a trade-off between the efficiency of the method and the security of the method. The SPDC source does not produce Fock state pairs (i.e., the probability distribution of the average photon number does not follow a Dirac delta distribution), but produces squeezed states with a residual multi-photon probability. Therefore, even if the average photon number of the source is n = 1, depending on the operating point, each emission event may result in 0 photons or 1 photon or more photons. A higher photon rate directly leads to a poorer single-photon purity ratio. That is to say, the SPDC emission process is non-deterministic in terms of the photon number. Therefore, it is not a deterministic source and does not implement a true single-photon source. This limits the distance for implementing the protocol, similar to the case for QKD [6].

[0008] As seen in reference [2], previous quantum time synchronization demonstrations were based on SPDC sources. However, these methods are based on non-deterministic sources (such as SPDC), use two sources of correlated photons, or require the use of dispersion-compensating fibers in the device. Summary of the Invention

[0009] One aspect of the present disclosure provides a method for determining an offset between a first time reference and a second time reference. The method includes: (i) obtaining information related to a detection time of a first photon in a first pair of photons at a first node and a detection time of a second photon in the first pair of photons at a second node, wherein the first pair of photons has been generated at the first node; (ii) obtaining information related to a detection time of a first photon in a second pair of photons at the first node and a detection time of a third photon at the first node, wherein the second pair of photons has been generated at the first node, and the third photon is received from the second node in response to sending a second photon in the second pair of photons to the second node; and (iii) determining, based on the obtained information, an offset between a first time reference at the first node and a second time reference at the second node.

[0010] Another aspect of the present disclosure provides a method implemented in a first node. The method includes: (i) generating a first pair of photons; (ii) obtaining information related to a detection time of a first photon in the first pair of photons at the first node; (iii) sending a second photon in the first pair of photons to a second node; (iv) obtaining information related to a detection time of the second photon in the first pair of photons at the second node; (v) generating a second pair of photons; (vi) obtaining information related to a detection time of a first photon in the second pair of photons at the first node; (vii) sending a second photon in the second pair of photons to the second node; (viii) obtaining information related to a detection time of a third photon at the first node, wherein the third photon is received from the second node in response to sending the second photon in the second pair of photons to the second node; and (ix) determining, based on the obtained information, an offset between a first time reference at the first node and a second time reference at the second node.

[0011] Another aspect of the present disclosure provides an apparatus for determining an offset between a first time reference and a second time reference. The apparatus is configured to: (i) obtain information related to a detection time of a first photon of a first pair of photons at a first node and a detection time of a second photon of the first pair of photons at a second node, wherein the first pair of photons has been generated at the first node; (ii) obtain information related to a detection time of a first photon of a second pair of photons at the first node and a detection time of a third photon at the first node, wherein the second pair of photons has been generated at the first node, and the third photon is received from the second node in response to sending a second photon of the second pair of photons to the second node; and (iii) determine an offset between a first time reference at the first node and a second time reference at the second node based on the obtained information.

[0012] Another aspect of the present disclosure provides a first node. The first node is configured to: (i) generate a first pair of photons; (ii) obtain information related to a detection time of a first photon of the first pair of photons at the first node; (iii) send a second photon of the first pair of photons to a second node; (iv) obtain information related to a detection time of the second photon of the first pair of photons at the second node; (v) generate a second pair of photons; (vi) obtain information related to a detection time of a first photon of the second pair of photons at the first node; (vii) send a second photon of the second pair of photons to the second node; (viii) obtain information related to a detection time of a third photon at the first node, wherein the third photon is received from the second node in response to sending the second photon of the second pair of photons to the second node; and (ix) determine an offset between a first time reference at the first node and a second time reference at the second node based on the obtained information. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] To better understand the examples of the present disclosure and to more clearly show how the examples may be implemented, reference will now be made, by way of example only, to the following drawings, in which:

[0014] Figure 1 is a flowchart of an example of a method 100 for determining an offset between a first time reference and a second time reference;

[0015] Figure 2 is a flowchart of an example of a method 200 for determining an offset between a first time reference and a second time reference implemented by a first node;

[0016] Figure 3Illustrated is a system 300 for determining an offset between a first time reference at a first node and a second time reference at a second node;

[0017] Figure 4 is a schematic diagram of an example of an apparatus 400 for determining an offset between a first time reference and a second time reference; and

[0018] Figure 5 is a schematic diagram of an example of a first node 500 for determining an offset between a first time reference at a first node 500 and a second time reference at a second node. Detailed Description

[0019] The following sets forth specific details, such as specific embodiments or examples for purposes of explanation and not limitation. Those skilled in the art will understand that other examples may be employed in addition to these specific details. In some instances, detailed descriptions of well-known methods, nodes, interfaces, circuits, and devices are omitted so as not to obscure the description with unnecessary detail. Those skilled in the art will understand that the described functionality may be implemented in one or more nodes using hardware circuits (e.g., analog and / or discrete logic gates interconnected to implement a dedicated function, ASIC, PLA, etc.) and / or using a software program and data in conjunction with one or more digital microprocessors or general purpose computers. Nodes that communicate using an air interface also have appropriate radio communication circuitry. Additionally, where appropriate, the technology may also be considered to be fully embodied in any form of computer-readable memory, such as solid-state memory, disk, or optical disk containing a set of appropriate computer instructions that would cause a processor to perform the techniques described herein.

[0020] Hardware implementations may include or encompass, but are not limited to, digital signal processor (DSP) hardware, reduced instruction set processors, hardware (e.g., digital or analog) circuits including, but not limited to, application specific integrated circuits (ASICs) and / or field programmable gate arrays (FPGAs), and (where appropriate) state machines capable of implementing such functionality.

[0021] Embodiments of the present disclosure relate to methods of time synchronization. Some embodiments of the present disclosure provide highly accurate (i.e., accurate to less than 260 - 265 nanoseconds) time synchronization methods demonstrated by quantum measurements using cascaded single photons. That is, these methods can be secure against spoofing by an adversary.

[0022] The example methods described herein can be used in accordance with a system including a first node (having a first time reference) and one or more second nodes, where the one or more second nodes can then receive highly accurate (i.e., accurate to less than 260 - 265 nanoseconds) time synchronization information from the first node. The one or more second nodes can be separated from the first node by kilometers of optical fiber.

[0023] The example methods herein use single photons from a cascaded three - level system (e.g., self - assembled quantum dots). As will be explained in more detail below, cascaded photon emission sources may be superior to other photon emission sources in generating single - photon states.

[0024] Furthermore, the generation time between the first photon and the second photon generated as a result of the cascade is unique (due to the randomness of the quantum system generating the photons). Thus, an external party will not be able to spoof the generation of the photon pair because the generation time of the second photon is unknown before the emission of the second photon.

[0025] Certain methods described herein can also be made secure against an adversary's spoofing by using entangled photon pairs. A Bell test can then be implemented to demonstrate that each photon in the entangled photon pair is generated by the first node and not by some intermediate party.

[0026] Embodiments of the present disclosure also utilize a photon emission source at the first node, but do not require a photon emission source at the second node. Thus, the systems described herein reduce the complexity and cost of the second node.

[0027] Certain systems described herein based on deterministic photon generation can generate a higher photon count (and thus shorten the acquisition time) for synchronization, while maintaining purity (due to the single - photon source) and thus maintaining the security of the protocol. The purity of the single - photon source also allows for a greater transmission distance compared to SPDC sources [6].

[0028] The deterministic nature of the emission also allows certain methods herein to reuse not only the correlation between photons emitted simultaneously (also referred to herein as "photon pairs" or "a pair of photons"), but also the correlation peaks (n to n + - 1) to improve the time resolution. In contrast, SPDC sources only use the correlation between photon pairs.

[0029] Optionally, a test (such as a Bell test) can also be run at a node (such as a user node), which involves multiple measurements of pairs of photons, and at least some of the pairs detected are entangled or generated at the same node, which comes with additional system complexity. In these embodiments, this provides additional security at the user node. For example, no photons are detected by a third party and re-emitted at a later time. By performing a Bell test on the reflected photons at the user node and at the source node, it can be demonstrated that no additional photons are injected into the optical fiber link.

[0030] Figure 1 FIG. 4 is a flowchart of an example of a method 100 for determining an offset between a first time reference and a second time reference. Method 100 includes: in step 102, obtaining information related to the detection time of a first photon in a first pair of photons at a first node and the detection time of a second photon in the first pair of photons at a second node, where the first pair of photons has been generated at the first node. In some embodiments, the first node sends the second photon in the first pair of photons to the second node. For example, the first node can send the second photon in the first pair of photons to the second node via an optical fiber.

[0031] The information related to the detection time of the first photon in the first pair of photons at the first node can be the time when the first photon in the first pair of photons is detected by a photodetector at the first node. For example, the information related to the detection time at the first node can include a time stamp of a first time reference generated after the photodetector detects the first photon. In some examples, the photodetector can include a superconducting nanowire single photon detector.

[0032] The information related to the detection time of the second photon in the first pair of photons at the second node can be the time when the second photon in the second pair of photons is detected by a photodetector at the second node. For example, the information related to the detection time at the second node can include a time stamp of a second time reference generated after the photodetector detects the second photon. In some examples, the photodetector can include a superconducting nanowire single photon detector.

[0033] In some embodiments, the second node can transmit the information related to the detection time of the second photon in the first pair of photons at the second node to the first node via a communication channel. The information can be transmitted to the first node via the deployed SMF.

[0034] In some embodiments, each pair of photons that has been generated at the first node is generated by a photon emission source. In some embodiments, the photon emission source includes a deterministic photon source.

[0035] In some embodiments, the photon emission source includes a source of time-correlated photons. The time-correlated photon source will emit pairs of time-correlated photons. It will be appreciated that using time-correlated photon pairs in the methods described herein prevents these methods from being easily spoofed. This time-correlation is not easily spoofed by an external attacker unless they are able to obtain a non-destructive measurement of one of the photons or a highly controlled single-photon source to create a similar emission lifetime.

[0036] In some embodiments, the photon emission source includes a source that emits photons by radiative decay.

[0037] In some embodiments, the photon emission source includes at least one quantum dot or quantum dot cascade. A quantum dot is an example of a photon emission source that is capable of generating entangled single-photon pairs. In some embodiments, the quantum dot generates photon pairs due to biexciton-exciton cascade decay.

[0038] The biexciton-exciton cascade decay will produce pairs of entangled single-photon states. The biexciton-exciton cascade decay is an example of a second-order decay, where the first photon in the photon pair always follows the second photon in the photon pair. Thus, a photon emission source that generates photons due to biexciton-exciton cascade decay will perform better in generating single-photon states than other photon emission sources. Additionally, since the generation time between the first photon and the second photon is unique (due to the randomness of the quantum system that generates the photons), an external party will not be able to spoof the generation of the photon pair because the generation time of the second photon is unknown prior to the emission of the second photon. This is in contrast to photon emission sources such as SPDC (where, when pairs of entangled single-photon states are generated by the source, they are emitted simultaneously), which may lead to the possibility of spoofing because the emission times of the photons are known.

[0039] It will be appreciated that although the exact emission times of the quantum dots according to the embodiments described herein will be uncertain (due to spontaneous decay in the cascade), after the emission of the two photons, the offset between two time references can be calculated via a two-photon correlation histogram derived from the accumulated detection events, thus providing an absolute time offset between the two time references, as will be described in more detail below.

[0040] In some embodiments, each pair of photons generated includes a pair of entangled photons. As will be explained in more detail below, using entangled photon pairs increases the security of the methods described herein.

[0041] In some embodiments, each pair of entangled photons is polarization-entangled. It will be appreciated that this polarization entanglement is not disrupted in an optical fiber and the photons can be sent along the optical fiber, although in some examples there may be some polarization rotation or noise, which will be described in more detail in this specification later.

[0042] Step 104 of method 100 includes: obtaining information related to the detection time of the first photon in the second pair of photons at the first node and the detection time of the third photon at the first node, where the second pair of photons has been generated at the first node, and the third photon is received from the second node in response to sending the second photon in the second pair of photons to the second node. For example, the first node may send the second photon in the second pair of photons to the second node via an optical fiber.

[0043] In some embodiments, the third photon is the second photon in the second pair of photons. For example, in some embodiments, the second photon in the second pair of photons is reflected towards the first node at the second node. Then, the second photon in the second pair of photons can reach the first node via an optical fiber.

[0044] It should be noted that the method described herein does not require the second node to include a photon emission source, nor does the second node require polarization optics. Therefore, the complexity and cost of the second node are reduced.

[0045] In some embodiments, where an entanglement test is performed at the second node, the second node may include the necessary polarization optics to enable the test to be performed.

[0046] The information related to the detection time of the first photon in the second pair of photons at the first node may be the time when the first photon in the second pair of photons is detected by a photodetector at the first node. For example, the information related to the detection time at the first node may include a timestamp generated after the photodetector detects the first photon. In some examples, the photodetector may include a superconducting nanowire single photon detector.

[0047] The information related to the detection time of the third photon at the first node may be the time when the third photon is detected by a photodetector at the first node. For example, the information related to the detection time at the first node may include a timestamp generated after the photodetector detects the third photon. In some examples, the photodetector may include a superconducting nanowire single photon detector.

[0048] Step 106 of method 100 includes: based on the obtained information, determining the offset between a first time reference (such as a first clock) at the first node and a second time reference (such as a second clock) at the second node. The first clock may be used by the first node to timestamp events (e.g., photon detection events). The second clock may be used by the second node to timestamp events (e.g., photon detection events).

[0049] In some embodiments, determining the offset based on the obtained information includes determining the offset based on the following: a first time difference between the detection time of the first photon in the first pair of photons at the first node and the detection time of the second photon in the first pair of photons at the second node, and a second time difference between the detection time of the first photon in the second pair of photons at the first node and the detection time of the third photon at the first node. That is to say, the above detection times can be used to determine the offset between the first clock at the first node and the second clock at the second node. It can be understood that the offset can represent the difference between the timestamp generated by the first clock for the first detection event and the timestamp generated by the second clock for the second detection event, where the first detection event and the second detection event occur at the same absolute time.

[0050] In some embodiments, the step of determining the offset between the first time reference at the first node and the second time reference at the second node based on the obtained information may include: performing step 102 and step 104 multiple times, and determining the offset between the first time reference at the first node and the second time reference at the second node based on the information obtained from each execution of step 102 and step 104.

[0051] For example, after repeatedly performing step 102, the cross-correlation of the difference between each detection time of the first photon at the first node and each corresponding detection time of the second photon at the second node will have peaks at values representing both the one-way travel time (of the photons) between the first node and the second node and the offset between the first time reference and the second time reference (which will be inherently reflected in the detection times).

[0052] For example, after repeatedly performing step 104, the cross-correlation of the difference between each detection time of the first photon at the first node and each corresponding detection time of the third photon at the first node will have a peak at a value representing the round-trip time between the first node and the second node. That is to say, this value allows the propagation time of the photons in the optical fiber to be calculated.

[0053] Then, these two values can be used to determine the absolute offset between the first time reference and the second time reference as follows:

[0054] In some embodiments, method 100 may be implemented by the first node. However, it can be understood that method 100 can be implemented by any node (e.g., the second node, or optionally, the third node).

[0055] In some embodiments, method 100 may further include: providing the determined offset to the second node.

[0056] In some embodiments, the second node can then synchronize its time reference (i.e., the second time reference) according to the determined offset that has been provided.

[0057] In some embodiments, method 100 further includes: performing a test on whether each photon in the generated first pair of photons is generated at the first node, or a test on whether the photons are entangled. For example, this can include: performing a Bell test, and based on the Bell test, determining whether each photon in the generated first pair of photons is generated at the first node. In some embodiments, method 100 further includes: performing a Bell test, and based on the Bell test, determining whether each photon in the generated second pair of photons is generated at the first node.

[0058] The Bell test enables the determination of the correspondence between the first photon and the second photon in each pair of photons, where the photon pairs are entangled photon pairs. In other words, the Bell test enables the determination of whether both the first photon and the second photon in a pair of photons are actually an entangled pair generated by a photon emission source.

[0059] That is to say, the Bell test can prove that the photons are generated by the provider, rather than by some intermediate party.

[0060] If the Bell test determines that the entanglement between the first photon and the second photon has degraded (or the photons are not entangled), then it can be assumed that an adversary may have intercepted at least one photon. After that, the detection times associated with these photons, or the determined offsets related to these detection times, can then be discarded.

[0061] In other words, using entangled photon pairs in the method described herein will improve the security of the method.

[0062] In some embodiments, an entanglement test is performed at the first node. For example, an entanglement test can be performed on the third photon and the first photon in the second pair of photons. This entanglement test can be used to verify that these photons are the original photons generated at the first node. In some embodiments, an entanglement test is performed at the second node. In some embodiments, an entanglement test can be performed on the first photon in the first pair of photons (which is detected at the first node) and the second photon in the first pair of photons (which is detected at the second node). This entanglement test can be used to verify that these photons are the original photons generated at the first node.

[0063] In some embodiments, performing the above two entanglement tests can verify that only the photons generated at the first node have been detected at the first node and the second node respectively. Therefore, this verification limits the attack surface to an asymmetric delay attack without additional loss, because the asymmetric loss in the channel can be detected by the number of photons measured.

[0064] Figure 2 It is a flowchart of an example of a method 200 for determining an offset between a first time reference and a second time reference implemented by a first node. The method 200 is an example implementation of the above method 100.

[0065] The method 200 includes generating a first pair of photons in step 202.

[0066] In some embodiments, each pair of photons generated by the first node is generated by a photon emission source. The photon emission source may correspond to any photon emission source described in the reference Figure 1 Any photon emission source described. The generated photons may also have any characteristics of the photons described in the reference Figure 1 Any characteristics of the photons described.

[0067] Step 204 of the method 200 includes: obtaining information related to the detection time of the first photon in the first pair of photons at the first node.

[0068] Step 206 of the method 200 includes: sending the second photon in the first pair of photons to a second node.

[0069] Step 208 of the method 200 includes: obtaining information related to the detection time of the second photon in the first pair of photons at the second node.

[0070] Step 210 of the method 200 includes: generating a second pair of photons.

[0071] Step 212 of the method 200 includes: obtaining information related to the detection time of the first photon in the second pair of photons at the first node.

[0072] Step 214 of the method 200 includes: sending the second photon in the second pair of photons to a second node.

[0073] Step 216 of the method 200 includes: obtaining information related to the detection time of a third photon at the first node, where the third photon is received from the second node in response to sending the second photon in the second pair of photons to the second node. As described in some embodiments in the reference Figure 1 The third photon is the second photon in the second pair of photons. In some embodiments, the second photon in the second pair of photons has been reflected towards the first node at the second node.

[0074] Step 218 of the method 200 includes: determining an offset between a first time reference at the first node and a second time reference at the second node based on the obtained information.

[0075] In some embodiments, method 200 further includes: performing a test to determine whether the generated first pair of photons or the generated second pair of photons are generated at the first node, or performing a test to determine whether the pair of photons are entangled. For example, method 200 may include: performing a Bell test; and based on the Bell test, determining whether each photon in the generated first pair of photons is generated at the first node. In some embodiments, method 200 further includes: performing a Bell test, and based on the Bell test, determining whether each photon in the generated second pair of photons is generated at the first node.

[0076] In some embodiments, the step of determining the offset based on the obtained information may include: determining the offset based on a first time difference between a detection time of a first photon in the first pair of photons at the first node and a detection time of a second photon in the first pair of photons at the second node, and a second time difference between a detection time of a first photon in the second pair of photons at the first node and a detection time of a third photon at the first node.

[0077] In some embodiments, the step of determining an offset between a first time reference at the first node and a second time reference at the second node based on the obtained information may include: performing steps 202 to 216 multiple times, and based on the information obtained from each execution of steps 202 to 206, determining an offset between a first time reference at the first node and a second time reference at the second node. For example, as referred to above Figure 1 as described, cross-correlation may be performed by the first node to determine an offset between a first time reference at the first node and a second time reference at the second node based on the obtained information.

[0078] In some embodiments, method 200 further includes: providing the determined offset to the second node.

[0079] Figure 3 A system 300 for determining an offset between a first time reference at a first node and a second time reference at a second node according to the method described herein is shown.

[0080] System 300 includes a first node (or master node) 302 and a second node (or user node) 304. In some embodiments, the first node 302 may be configured to perform any one of the above methods 100 or 200. In some embodiments, the second node 304 may be configured to perform the above method 100. In the illustrated embodiment, the first node 302 determines an offset between a first time reference at the first node and a second time reference at the second node according to the above method 100.

[0081] The first node 302 can then provide the determined offset to the second node 304. For example, the offset can be provided to the second node 304 via the deployed SMF or via an optional communication channel.

[0082] The first node 302 includes a photon emission source 306. The photon emission source 206 includes an 80 MHz pulsed laser 308, a beam splitter 310, a quantum dot 312 included within a cryostat, and a spectral selector 314. In the illustrated embodiment, the quantum dot 312 is capable of generating deterministic, time-correlated entangled single photon pairs by means of biexciton-exciton cascade decay. In this example, the quantum dot 312 emits in the C band.

[0083] Examples of quantum dots 312 can be found in [3]. Examples of correlation diagrams between photon pairs emitted by such a source can be found in [4].

[0084] It will be appreciated that in other embodiments, an optional photon emission source may be included within the first node 302. For example, the photon emission source can include cascade emission within an atomic system [7]. In another example, the photon emission source can include a biexciton-exciton cascade within a 2D material system.

[0085] The second node 304 includes a time-to-digital converter 322 connected to a 10 MHz reference signal, a photodetector 320, a notch filter 318, and a reflector 316.

[0086] In the illustrated embodiment, the light emitted by the pulsed laser 308 is split by the beam splitter 310 such that a certain proportion of the light stimulates the quantum dot 312. This stimulation then triggers biexciton-exciton cascade decay, thereby generating a pair of entangled single photon states.

[0087] The pair of entangled single photon states is then coupled back to and reflected by the beam splitter 310 such that they are then transmitted to the spectral selector 314.

[0088] The spectral selector 314 then only allows the pair of entangled single photon states to pass such that the first photon of the pair is coupled into the optical fiber 324 and the second photon of the pair is coupled into the optical fiber 326.

[0089] Then, the first photon of the pair is sent via the optical fiber 326 to the master clock node 328. The master clock node 328 is included within the first node 302. The master clock node 328 includes a time-to-digital converter 332 and a photodetector 330 connected to a 10 MHz reference signal.

[0090] The second photon of the pair of photons is sent to the circulator 334 included within the first node 302, and then the circulator 334 sends the second photon to the second node 304 via the optical fiber 336.

[0091] Then, the first photon of the pair of photons is detected by the optical detector 330 at the first node 302. In this example, the optical detector 330 includes a superconducting nanowire single photon detector. However, it can be understood that an optional suitable optical detector can be provided. Then, the signal from the optical detector 330 is timestamped by the time-to-digital converter 332.

[0092] The second photon of the pair of photons reaches the reflector 316. In this embodiment, the reflector 316 is a 70 / 30 optical fiber reflector. That is, the reflector 316 is configured to reflect 70% of the photons back to the first node 302 and allow 30% of the photons to be transmitted to the notch filter 318. The notch filter 318 filters out any other signals that may be present in the optical fiber network.

[0093] If the second photon is reflected by the reflector 316, it returns to the circulator 326 at the first node 302 via the optical fiber 336, which then causes the second photon to be sent to the master clock node 328 via the optical fiber 338.

[0094] Then, the second photon of the pair of photons is detected by the optical detector 330 at the first node 302, and the detection time is timestamped by the time-to-digital converter 332.

[0095] If the second photon is transmitted to the notch filter 318, the notch filter 318 then transmits the second photon to the optical detector 320, and the detection time is timestamped by the time-to-digital converter 322.

[0096] That is, for each pair of photons generated, both the first photon and the second photon of the photon pair will be detected at the first node 302, or the first photon of the photon pair will be detected at the first node 302, and the second photon of the photon pair will be detected at the second node 304.

[0097] The second node 304 can transmit information related to the detection time of the second photon of a pair of photons at the second node 302 to the first node 302 via a communication channel. For example, this information can be transmitted to the first node 302 via a traditional communication network.

[0098] That is, information related to the detection time of the first photon in the first pair of photons at the first node 302 and the detection time of the second photon in the first pair of photons at the second node 304 is obtained, where the first pair of photons has been generated at the first node 302, and information related to the detection time of the first photon in the second pair of photons at the first node 302 and the detection time of the third photon at the first node 302 is obtained, where the second pair of photons has been generated at the first node 302, and the third photon is received from the second node 304 in response to sending the second photon in the second pair of photons to the second node 304. In the illustrated embodiment, this information is obtained by the first node 302. However, as described above, the information related to the above detection times can be obtained by the second node 304 or the third node.

[0099] As described above, the above information related to the detection time can be obtained for multiple pairs of photons (i.e., information can be obtained regarding multiple instances where the first photon in a pair of photons is detected at the first node 302 and the second photon in the pair of photons is detected at the second node 304, and information can be obtained regarding multiple instances where the first photon in a pair of photons is detected at the first node 302 and the third photon is detected at the first node 302).

[0100] Then, the cross-correlation of the differences between each detection time of the first photon at the first node 302 and each corresponding detection time of the second photon at the second node 304, and the cross-correlation of the differences between each detection time of the first photon at the first node 302 and each corresponding detection time of the third photon at the first node 302 can be used to determine the absolute offset between the first time reference at the first node 302 and the second time reference at the second node 304 (as described above with reference to step 106). It can be understood that the accuracy of the method performed by the reference system 300 will be limited by the accuracy of the 10 MHz frequency reference.

[0101] That is, the offset between the first time reference at the first node 302 and the second time reference at the second node 304 is determined based on the obtained information. In this example, this step is implemented by the first node 302. However, as described above, the second node 304 or the third node can alternatively implement this step (if the information related to the above detection times is obtained by these nodes respectively).

[0102] Then, the determined offset can be provided by the first node 302 to the second node 304. Then, the determined offset can be used by the second node 304 to synchronize the second time reference.

[0103] As described in reference method 100, the method performed by reference system 300 is protected by the temporal correlation between the first photon and the second photon in each photon pair. Since each pair of photons generated is entangled, tests (such as a Bell test) can be implemented to verify the entanglement between the first photon and the second photon in each pair, thus proving the origin of the emitted photons and rendering any attack based on photon measurement ineffective.

[0104] Accordingly, the test will indicate whether an attacker has attempted to interfere with the photons (since the test will determine that the entanglement of the entangled photon pairs has degraded), or whether the photons have been added by the attacker himself (since the detection will confirm that the origin of the added photons is not the first node 302).

[0105] Therefore, the use of entangled photon pairs can enhance the security of the method.

[0106] An example of how an adversary might attempt to introduce delay into system 300 is now described. The adversary might attempt to introduce some delay into the system by reflecting some photons back to the first node 302 while forwarding the remaining photons to the second node 304. Although the optical detector at the first node will not be able to resolve whether the photons have been reflected by the adversary, since the photons are deterministically generated at the first node 302, in addition to the loss of the line (which is half of the loss experienced in the line due to the photons passing through the line twice in opposite directions), the photons reflected by the second node 304 can be counted. As a result, the second node 304 can be informed of how many photons should be expected to arrive at the second node 304.

[0107] If fewer photons than expected arrive at the second node 304, it can be determined that there may be an attacker in the loop. After that, the previously obtained detection times or the previously determined offsets related to these detection times can be discarded.

[0108] As described above, each pair of entangled photons can be polarization-entangled. It can be understood that the polarization entanglement of a pair of entangled photons is not destroyed in an optical fiber (the photons can be sent to the first and second nodes through the optical fiber), thus allowing tests to be implemented to prove the origin of the emitted photons. It can be understood that in embodiments where the counting rate (for the detected photon pairs) and the polarization change rate in the optical fiber have appropriate values, it is not necessary to correct for optical fiber polarization drift in order to implement the test.

[0109] It can be understood that the main causes of decoherence in an optical fiber are photon absorption and dissipation. However, to counteract these effects, only coincidences (i.e., instances where both photons in a pair of photons are detected) are considered for the entanglement tests described herein.

[0110] Note that polarization drift in the deployed optical fiber can be slow. In reference [5], the average polarization change of the measured optical fiber is 0.759% ± 0.409% per hour, which can be corrected before performing the entanglement test. Reference [5] also describes a gradient descent algorithm for polarization stabilization.

[0111] Now consider dispersion. For a dispersion rate of 1 Gbit / s in an optical fiber, photons can typically travel 55 - 60 km in the fiber before dispersion compensation is required. For a dispersion rate of 10 Gbit / s, the distance is approximately 40 km. For a dispersion rate of 40 Gbit / s, the distance is approximately 5 km.

[0112] For Figure 3 For the system 300 shown in , for one-way transmission, the dispersion experienced by a pulse with a 5 GHz bandwidth can be estimated as 20 ps / (nm km) * 0.04 nm * 100 km = 80 ps. Note also that dispersion can be corrected using mechanisms such as FBG-based modules, post-distributed or pre-distributed compensation, DSP, and / or multi-core optical fibers with a specific refractive index profile.

[0113] It should be noted that the above examples illustrate rather than limit the invention, and those skilled in the art will be able to design many alternative examples without departing from the scope of the appended claims. The phrase "comprising" does not exclude the presence of other elements or steps in addition to those listed in the claims, "a" or "an" does not exclude a plurality, and a single processor or other unit can implement the functions of several units recited in the following claims. When using terms such as "first", "second", etc., they should only be understood as labels for facilitating the identification of specific features. In particular, unless otherwise clearly stated, they should not be construed as describing the first or second of multiple such features (i.e., the first or second such feature to occur in time or space). Unless otherwise clearly stated, the steps in the methods disclosed herein can be performed in any order. Any reference signs in the claims should not be construed as limiting their scope.

[0114] Figure 4 is a schematic diagram of an example of an apparatus 400 for determining the offset between a first time reference and a second time reference. The apparatus 400 includes a processing circuit 402 (e.g., one or more processors) and a memory 404 communicatively coupled to the processing circuit 402. The memory 404 contains instructions executable by the processing circuit 402. The apparatus 400 also includes an interface 406 communicatively coupled to the processing circuit 402. Although the interface 406, the processing circuit 402, and the memory 404 are shown as being connected in series, they may alternatively be interconnected in any other manner, such as via a bus.

[0115] In one embodiment, the memory 404 includes instructions executable by the processing circuitry 402 such that the apparatus 400 is operable to obtain information related to a detection time of a first photon of a first pair of photons at a first node and a detection time of a second photon of the first pair of photons at a second node, wherein the first pair of photons has been generated at the first node; obtain information related to a detection time of a first photon of a second pair of photons at the first node and a detection time of a third photon at the first node, wherein the second pair of photons has been generated at the first node and the third photon is received from the second node in response to sending a second photon of the second pair of photons to the second node; and based on the obtained information, determine an offset between a first time reference at the first node and a second time reference at the second node.

[0116] In some examples, the apparatus 400 is operable to perform the methods 100 and 200 described above with reference to Figure 1 and Figure 2 the methods 100 and 200 described.

[0117] Figure 5 FIG. is a schematic diagram of an example of a first node 500 for determining an offset between a first time reference at a first node 500 and a second time reference at a second node. The first node 500 includes processing circuitry 502 (e.g., one or more processors) and a memory 504 communicatively coupled to the processing circuitry 502. The memory 504 includes instructions executable by the processing circuitry 502. The first node 500 also includes an interface 506 communicatively coupled to the processing circuitry 502. Although the interface 506, the processing circuitry 502, and the memory 504 are shown as being serially connected, they may alternatively be interconnected in any other manner, such as via a bus.

[0118] In one embodiment, the memory 504 includes instructions executable by the processing circuitry 502 such that the first node 500 is operable to: generate a first pair of photons; obtain information related to a detection time of a first photon of the first pair of photons at the first node; send a second photon of the first pair of photons to the second node; obtain information related to a detection time of the second photon of the first pair of photons at the second node; generate a second pair of photons; obtain information related to a detection time of a first photon of the second pair of photons at the first node; send a second photon of the second pair of photons to the second node; obtain information related to a detection time of a third photon at the first node, wherein the third photon is received from the second node in response to sending a second photon of the second pair of photons to the second node; and based on the obtained information, determine an offset between a first time reference at the first node and a second time reference at the second node.

[0119] In some examples, the first node 500 is operable to perform the above reference Figure 2 Method 200 is described.

[0120] Abbreviations

[0121] GNSS Global Navigation Satellite System

[0122] OAS Over-the-Air Synchronization

[0123] PTP Precision Time Protocol

[0124] T-GM Telecom Master Control

[0125] TDD Time Division Duplex

[0126] TAE relative time error

[0127] TTOF Time Transfer over Fiber

[0128] TWTTOF Bidirectional Transmission over Fiber

[0129] SPDC Spontaneous Parametric Down Conversion

[0130] SSSPD Superconducting Nanowire Single Photon Detector

[0131] QD Quantum Dots

[0132] KTH Royal Institute of Technology

[0133] BS Beam Splitter

[0134] NF Notch Filter

[0135] TG Transmission Grating

[0136] T Transmission

[0137] R Reflectivity

[0138] References

[0139] 1. Stefano Ruffini et al, 5G synchronization requirements and solutions, Ericsson Technology review, #01, 2021

[0140] 2. F. Hou et al., Fiber-optic two-way quantum time transfer with frequency-entangled pulses, Phys. Rev. A 100, 023849

[0141] 3. Müller, M., Bounouar, S., K. et al. On-demand generation of indistinguishable polarization-entangled photon pairs. Nature Photon 8, 224 - 228 (2014). https: / / doi.org / 10.1038 / nphoton.2013.377

[0142] 4. Zeuner, Katharina D., et al. "A stable wavelength-tunable triggered source of single photons and cascaded photon pairs at the telecom C-band." Applied Physics Letters 112.17 (2018): 173102.

[0143] 5. Ekemar, L. (2020). Polarization stabilization for quantum key distribution in deployed fibre (Dissertation). Retrieved from http: / / urn.kb.se / resolve?urn=urn:nbn:se: kth:diva-279632

[0144] 6. Bozzio, M., Vyvlecka, M., Cosacchi, M. et al. Enhancing quantum cryptography with quantum dot single-photon sources. npj Quantum Inf 8, 104 (2022). https: / / doi.org / 10.1038 / s41534-022- 00626-z

[0145] 7. Aspect, Alain, Philippe Grangier, and Gérard Roger. "Experimental tests of realistic local theories via Bell's theorem." Physical review letters 47.7 (1981): 460.

Claims

1. A method for determining an offset between a first time reference and a second time reference, the method comprising: (i) obtaining information related to a detection time of a first photon of a first pair of photons at a first node and a detection time of a second photon of the first pair of photons at a second node, wherein the first pair of photons has been generated at the first node; (ii) obtaining information related to a detection time of a first photon of a second pair of photons at the first node and a detection time of a third photon at the first node, wherein the second pair of photons has been generated at the first node, and the third photon is received at the first node in response to sending a second photon of the second pair of photons to the second node; and (iii) determining, based on the obtained information, an offset between a first time reference at the first node and a second time reference at the second node.

2. The method according to claim 1, wherein The first node sends the second photon of the first pair of photons to the second node.

3. The method according to claim 1 or 2, wherein The first node sends the second photon of the second pair of photons to the second node.

4. The method according to any one of the preceding claims, wherein The method is implemented by the first node.

5. The method according to any one of the preceding claims, wherein, The third photon is the second photon of the second pair of photons.

6. The method according to claim 5, wherein, The second photon of the second pair of photons has been reflected towards the first node at the second node.

7. The method according to any one of the preceding claims, wherein, Each generated pair of photons is generated by a photon emission source.

8. The method according to claim 7, wherein The photon emission source includes a deterministic photon source.

9. The method according to claim 7 or 8, wherein The photon emission source includes a source of time-correlated photons.

10. The method according to any one of claims 7-9, wherein, The photon emission source includes a source that emits photons through radiative decay.

11. The method according to any one of claims 7-10, wherein, The photon emission source includes at least one quantum dot or quantum dot cascade.

12. The method according to any one of the preceding claims, wherein, Each generated pair of photons includes a pair of time-correlated photons.

13. The method according to any one of the preceding claims, wherein, Each generated pair of photons includes a pair of entangled photons.

14. The method according to claim 13, wherein, Each pair of entangled photons is polarization-entangled.

15. The method according to claim 13 or 14, wherein The method further comprises: determining whether each photon of the first generated pair of photons is generated and / or entangled at the first node.

16. The method according to any one of claims 13 - 15, wherein, The method further comprises: determining whether each photon of the second generated pair of photons is generated and / or entangled at the first node.

17. The method according to claim 15 or 16, wherein The determination is implemented at the first node.

18. The method according to claim 15 or 16, wherein, The determination is implemented at the second node.

19. The method according to any one of the preceding claims, wherein, Determining the offset based on the obtained information includes: determining the offset based on: a first time difference between the detection time of the first photon of the first pair of photons at the first node and the detection time of the second photon of the first pair of photons at the second node; and a second time difference between the detection time of the first photon of the second pair of photons at the first node and the detection time of the third photon at the first node.

20. The method according to any one of the preceding claims, wherein, The method further comprises: providing the determined offset to the second node.

21. The method according to any one of the preceding claims, wherein, The step of determining an offset between a first time reference at the first node and a second time reference at the second node based on the obtained information includes: performing step (i) and step (ii) multiple times; and Based on the information obtained from each execution of step (i) and step (ii), determine the offset between the first time reference at the first node and the second time reference at the second node.

22. A method implemented in a first node, the method comprising: (i) Generate a first pair of photons; (ii) Obtain information related to the detection time of the first photon in the first pair of photons at the first node; (iii) Send the second photon in the first pair of photons to a second node; (iv) Obtain information related to the detection time of the second photon in the first pair of photons at the second node; (v) Generate a second pair of photons; (vi) Obtain information related to the detection time of the first photon in the second pair of photons at the first node; (vii) Send the second photon in the second pair of photons to the second node; (viii) Obtain information related to the detection time of a third photon at the first node, where the third photon is received from the second node in response to sending the second photon in the second pair of photons to the second node; And (ix) Based on the information obtained, determine the offset between the first time reference at the first node and the second time reference at the second node.

23. The method according to claim 22, wherein, The third photon is the second photon in the second pair of photons.

24. The method according to claim 23, wherein, The second photon in the second pair of photons has been reflected towards the first node at the second node.

25. The method according to any one of claims 22 to 24, wherein, Each pair of photons generated is generated by a photon emission source.

26. The method according to claim 25, wherein The photon emission source includes a deterministic photon source.

27. The method according to claim 25 or 26, wherein The photon emission source includes a source of time-correlated photons.

28. The method according to any one of claims 25-27, wherein, The photon emission source includes a source that emits photons through radiative decay.

29. The method according to any one of claims 25 - 28, wherein The photon emission source includes at least one quantum dot or quantum dot cascade.

30. The method according to any one of claims 22-29, wherein, Each pair of photons generated includes a pair of time-correlated photons.

31. The method according to any one of claims 22 - 30, wherein Each pair of photons generated includes a pair of entangled photons.

32. The method according to claim 31, wherein, Each pair of entangled photons is polarization-entangled.

33. The method according to claim 31 or 32, wherein The method further comprises: Determine whether each photon in the first pair of photons generated is generated and / or entangled at the first node.

34. The method according to any one of claims 31 to 33, wherein The method further comprises: Determine whether each photon in the second pair of photons generated is generated and / or entangled at the first node.

35. The method according to any one of claims 22-34, wherein, Determining the offset based on the information obtained includes: Determining the offset based on: A first time difference between the detection time of the first photon in the first pair of photons at the first node and the detection time of the second photon in the first pair of photons at the second node; and A second time difference between the detection time of the first photon in the second pair of photons at the first node and the detection time of the third photon at the first node.

36. The method according to any one of claims 22-35, wherein, The method further comprises: Provide the determined offset to the second node.

37. The method according to any one of claims 22-36, wherein, The step of determining the offset between the first time reference at the first node and the second time reference at the second node based on the information obtained includes: Execute steps (i) to (viii) multiple times; and Based on the information obtained in each execution from step (i) to step (viii), determine the offset between the first time reference at the first node and the second time reference at the second node.

38. A computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to perform the method according to any one of the preceding claims.

39. A computer program product comprising a non-transitory computer-readable medium having stored thereon the computer program according to claim 38.

40. A device for determining the offset between a first time reference and a second time reference, the device being configured to: (i) Obtain information related to the detection time of the first photon in the first pair of photons at the first node and the detection time of the second photon in the first pair of photons at the second node, wherein, The first pair of photons has been generated at the first node; (ii) Obtain information related to the detection time of the first photon in the second pair of photons at the first node and the detection time of the third photon at the first node, wherein the second pair of photons has been generated at the first node, and the third photon is received from the second node in response to sending the second photon in the second pair of photons to the second node; And (iii) Based on the obtained information, determine the offset between the first time reference at the first node and the second time reference at the second node.

41. The apparatus according to claim 40, wherein, The device is further configured to implement the method according to any one of claims 2 - 21.

42. A first node, the first node being configured to: (i) Generate a first pair of photons; (ii) Obtain information related to the detection time of the first photon in the first pair of photons at the first node; (iii) Send the second photon in the first pair of photons to a second node; (iv) Obtain information related to the detection time of the second photon in the first pair of photons at the second node; (v) Generate a second pair of photons; (vi) Obtain information related to the detection time of the first photon in the second pair of photons at the first node; (vii) Send the second photon in the second pair of photons to the second node; (viii) Obtain information related to the detection time of the third photon at the first node, wherein The third photon is received from the second node in response to sending the second photon in the second pair of photons to the second node; And (ix) Based on the obtained information, determine the offset between the first time reference at the first node and the second time reference at the second node.

43. The apparatus according to claim 42, wherein, The device is further configured to implement the method according to any one of claims 23 - 37.

Images