Teleportation system for the quantum internet

Abstract

Quantum teleportation is essential for many quantum information technologies, including long-distance quantum networks. We realize conditional quantum teleportation of time-binned qubits at a telecommunication wavelength of 1536.5 nm using a fiber-coupled device including state-of-the-art low-noise superconducting nanowire single-photon detectors and commercially available optics. We measure teleportation fidelity better than 90%, consistent with an analytical model of our system including realistic imperfections. To demonstrate the compatibility of our setup with deployed quantum networks, we teleported a qubit over 22 km of single-mode fiber while transmitting the qubit over another 22 km of fiber. Our system is compatible with emerging solid-state quantum devices and provides a realistic foundation for a high-fidelity quantum internet using practical devices.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims the benefit under 35 U.S.C. § 119(e) of co-pending and commonly assigned U.S. Provisional Patent Application No. 63 / 285,782 entitled TELEPORTATION SYSTEMS TOWARD A QUANTUM INTERNET (CIT-8635), filed on December 3, 2021 by Maria Spiropulu and Venkata Ramana Raju Valivarthi, which is incorporated herein by reference.

[0002] (Federal Funding Statement) (Research and Development) This invention was made with Government support under Grant Nos. DE-SC0019219 and DE-SC0020376 awarded by the U.S. Department of Energy. The Government has certain rights in this invention.

[0003] (1. Technical Field) The present invention relates to a quantum teleportation system and a method for manufacturing the same. [Background technology]

[0004] 2. Description of Related Art The purpose of a quantum network is to distribute qubits of quantum information between different locations, which is a key task for quantum cryptography, distributed quantum computing and sensing. Quantum networks are expected to form part of the future quantum internet [20-22]. A quantum network is a globally distributed set of quantum processors, sensors or their users, interconnected over a network that can allocate quantum resources (e.g., qubits and entangled states) between locations. Many quantum network architectures require quantum teleportation protocols, such as star networks that distribute entanglement from a central location or quantum repeaters that overcome the error tradeoff of direct transmission of quantum information [19, 23-26].

[0005] Quantum teleportation of a qubit can be achieved by performing a Bell-state measurement (BSM) between the qubit and another qubit that forms one member of an entangled Bell state [1,18,27]. The quality of teleportation is often characterized by the fidelity F = 〈ψ|ρ|ψ〉 of the teleported state to the state achieved by ideal generation and teleportation, |ψ〉

[15] . This metric will become increasingly important as quantum networks move beyond specific applications such as quantum key distribution and towards a quantum internet.

[0006] Polarization-based qubits are favored for demonstrating quantum teleportation over free-space channels [Refs. 28-30], including the recent ground-to-satellite quantum teleportation [Ref. 31], because they have no polarization rotation in free space and are easy to prepare and measure. Qubits encoded by the arrival times of individual photons, i.e., time-bin qubits [Ref. 32], are useful for fiber networks because of their ease of generation, interfacing with quantum devices, and independence from the dynamic polarization transformations of real fibers. Individual telecommunication-band photons (wavelengths of about 1.5 μm) are ideal carriers for qubits in networks because of their ability to travel rapidly over long distances in deployed optical fibers [Refs. 17, 33-35] or atmospheric channels [Ref. 36]. Furthermore, improvements and increasing availability of sources and detectors of individual telecommunication-band photons are accelerating progress toward practical quantum networks and related technologies such as quantum memories [Ref. 37], transducers [Refs. 38, 39], and quantum nondestructive measurement devices [Ref. 40]. Summary of the Invention [Problem to be solved by the invention]

[0007] Teleportation of telecommunication-band photonic time-bin qubits has been performed in and outside the laboratory with impressive results [Refs. 33–35, 41–46]. Nevertheless, little work has been done to increase the F of these qubits to above approximately 90%, especially using practical devices (e.g., using fiber-coupled commercial devices) that would allow for easy replication and deployment of quantum networks. Furthermore, for the quantum internet, it is desirable to develop teleportation systems that are compatible with new quantum devices. [Means for solving the problem]

[0008] Examples of systems and methods according to the present invention include, but are not limited to, the following.

[0009] [Example 1] 1. A quantum teleportation system comprising: a transmitter that generates a first photon; a source of pairs of entangled photons, each pair including a second photon entangled with a third photon; a coupler electromagnetically coupled to the transmitter and to a source of entangled photon pairs; a pair of detectors D1 and D2 electromagnetically coupled to a coupler; a receiver including a detection system including a detector D3 for detecting a third photon; an optical fiber connecting a detector D3 and a source of entangled photon pairs, the detector D3 detecting a third photon transmitted along the optical fiber; a clock distribution system that outputs one or more clock signals that control timing of the first photon, the second photon, and the third photon; a coupler for interacting one of the first photons carrying the first quantum bit and one of the second photons carrying the second quantum bit to form interference; a pair of detectors D1 and D2 detect interference used to obtain a Bell state measurement of a quantum system including a first qubit and a second qubit; Detector D3 detects one of the third photons intertwined with one of the second photons and outputs a signal in response thereto; and A detection system reads the state of the first qubit using the signal and a Bell state measurement. a clock distribution system that outputs the clock signal; a data collection system that collects arrival times of the first and second photons at detectors D1 and D2 and the arrival time of the third photon at detector D3, the arrival times being tagged with reference to a clock signal such that one or more sets of photons are identified, each set including one of the first photons, one of the second photons, and one of the third photons; and a computer for benchmarking the quantum teleportation system in real time using arrival times, the benchmarking including using a model to simulate at least one of the fidelity of the teleportation of a first qubit teleported to one of the third photons received at detector D3, or the degree of indistinguishability between one of the first photons and one of the second photons as a function of the average number of second photons, the model being calibrated and validated using experimental measurements of the teleportation fidelity and the degree of indistinguishability; A quantum teleportation system comprising:

[0010] [Example 2] In the system described in Example 1, a transmitter generating pulses of electromagnetic radiation each including one or more first photons; The system further comprises: a first attenuator that attenuates pulses of electromagnetic radiation to output attenuated pulses each including a first average number of first photons, the first average number of first photons received at the combiner increasing a likelihood that the combiner will cause one of the first photons to interact with one of the second photons to form interference; a first filter electromagnetically coupled to the coupler and configured to spectrally filter the electromagnetic radiation to increase indistinguishability between one of the first photons and one of the second photons; one or more second filters electromagnetically coupled to the source of entangled photon pairs and configured to spectrally filter the entangled photons; Equipped with the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early and a late arriving photon; and The source of the entangled photons includes a laser that excites a nonlinear material to output second photons, including idler photons, and third photons, including signal photons, according to a spontaneous parametric down conversion (SPDC) process. It is a system.

[0011] [Example 3] In the system described in Example 1, benchmarking includes determining at least one of the following: a fidelity of teleportation of a first quantum bit teleported to one of the third photons received at D3, a degree of indistinguishability between one of the first photons and one of the second photons, or a coincident photon detection rate of three times that of one of the photons detected in coincidence at each of D1, D2 and D2, the system.

[0012] [Example 4] In the system described in Example 1, the combiner includes a beam splitter or a linear optical device capable of interfering photons or electromagnetic fields.

[0013] [Example 5] In the system described in Example 1, the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early and a late arriving photon; the source of entangled photons includes a laser that excites the nonlinear material to output one of the second photons including an idler photon and one of the third photons including a signal photon according to a spontaneous parametric down-conversion (SPDC) process; The clock signal includes a clock cycle. The data acquisition system measures the average number of second photons by comparing: a coincidence rate involving events in which one of the second photons and one of the third photons in one of the entangled photon pairs are detected in the same one of the clock cycles; and the contingency rate involving an event in which one of the second photons and one of the third photons in one of the entangled photon pairs are detected in different clock cycles; Measure the average number of second photons by comparing The degree of indistinguishability was measured by performing the Hong-Ou-Mandel experiment, which uses a coupler containing a beam splitter to observe interference, and The fidelity of the teleportation is measured using an interferometer, which measures the visibility of the third photon's interference with itself. It is a system.

[0014] [Example 6] In the system described in Example 5, the model calculates the fidelity and indistinguishability of the teleportation, and this calculation is The probability P of coincident detection of one-triple of photons in each of the detectors D1, D2 and D3 3f , i.e.

number

[0015] [Example 7] In the system described in Example 6,

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[0016] [Example 8] In the system described in Example 7, the first qubit comprises a first time bin qubit, the second qubit comprises a second time bin qubit; The clock signal includes a clock cycle. The data collection system is a coincidence rate that includes events in which one of the second photons and one of the third photons in one of the entangled photon pairs are detected in the same one of the clock cycles; and an accidental rate that includes an event in which one of the second photons and one of the third photons in one of the entangled photon pairs are detected in different clock cycles; and a first detection rate of the second photons; and a second detection rate of the third photon; and Get η i is the second detection rate divided by the concordance rate, and η s is the first detection rate divided by the match rate, and The average number of second photons per time bin is the coincidence rate divided by the coincidence rate for the system.

[0017] [Example 9] In the system described in Example 4, the model calculates the probability that detectors D1, D2 and D3 receive one of the first photons, one of the second photons and one of the third photons in the same clock cycle using fitting parameters including transmittances representing indistinguishable quantities.

[0018] [Example 10] In the system described in Example 2, the computer uses the benchmark to output feedback used to optimize at least one of the timing, the intensity of the entangled photons output from the source of entangled photons, the spectral filtering of the photons, or the attenuation of the pulse of electromagnetic radiation so as to achieve a teleportation fidelity of greater than 0.90 when the third photon travels a distance of at least 22 kilometers along the optical fiber, the system.

[0019] [Example 11] The system of Example 1, further comprising a display for displaying the benchmark.

[0020] [Example 12] 1. A method of teleporting using a quantum teleportation system, comprising: teleporting the first quantum bit, the teleporting comprising: performing a Bell state measurement of a quantum system comprising interfering one or more first photons carrying a first quantum bit and one or more second photons carrying a second quantum bit, the quantum system including one of the first photons and one of the second photons; detecting one or more third photons, each of the third photons being confounded with one of the second photons prior to the interfering step; reading out the state of the first qubit using a Bell state measurement; obtaining arrival times of the first and second photons at detectors D1, D2 used to perform a Bell state measurement and the arrival time of the third photon at the receiver, the arrival times being tagged with reference to a clock signal such that one or more sets of photons may be identified, each set including one of the first photons, one of the second photons and one of the third photons; reading the state of the first quantum bit; and benchmarking the quantum teleportation system in real time using the arrival times; A method comprising:

[0021] [Example 13] 1. A computer implemented system comprising one or more processors, one or more memories, and an application stored in the one or more memories, The application is executed by one or more processors to benchmark a quantum teleportation system in real time, the quantum teleportation system comprising: teleporting a first quantum bit, performing a Bell state measurement of a quantum system, the measurement comprising the sub-steps of interfering one or more first photons carrying a first quantum bit and one or more second photons carrying a second quantum bit, the quantum system including one of the first photons and one of the second photons; detecting one or more third photons at the receiver, each of the third photons being entangled with one of the second photons prior to interference; teleporting the first quantum bit; reading out the state of the first qubit using a Bell state measurement; The purpose of the present invention is to carry out the following: The benchmarking includes the application, the application comprising: receiving arrival times of the first and second photons at detectors D1, D2 used to perform the Bell state measurement, and the arrival time of the third photon at the receiver, the arrival times tagged with reference to a clock signal such that one or more sets of photons can be identified, each set including one of the first photons, one of the second photons and one of the third photons; using the arrival times to determine at least one of: a fidelity of teleportation of the first quantum bit teleported to one of the third photons received at D3, a degree of indistinguishability of one of the first photons and one of the second photons, or a three-fold coincident photon detection rate where one of the photons is detected coincidentally at each of D1, D2, and D2; 4. A computer-implemented system for

[0022] [Example 14] 1. A computer-implemented method comprising: benchmarking a quantum teleportation system in real time, the teleportation system comprising: teleporting a first quantum bit, performing a Bell state measurement of a quantum system, the method comprising the sub-steps of interfering one or more first photons carrying a first quantum bit and one or more second photons carrying a second quantum bit, the quantum system including one of the first photons and one of the second photons; detecting one or more third photons, each third photon being confounded with one of the second photons prior to the interfering substep; teleporting the first quantum bit; reading out the state of the first qubit using a Bell state measurement; The purpose of the present invention is to carry out the following: The step of benchmarking includes the application, the application comprising: receiving arrival times of the first and second photons at detectors D1, D2 used to perform the Bell state measurement, and the arrival time of the third photon at the receiver, the arrival times being tagged with reference to a clock signal such that one or more sets of photons may be identified, each set including one of the first photons, one of the second photons and one of the third photons; and using the arrival times to determine at least one of: a fidelity of teleportation of the first quantum bit teleported to one of the third photons received at detector D3; a degree of indistinguishability between one of the first photons and one of the second photons; and a three-fold coincidence photon detection rate where one of the photons is detected at each of detectors D1, D2 and D2. A computer-implemented method comprising:

[0023] [Example 15] In the system or method of Example 13 or 14, a transmitter generating pulses of electromagnetic radiation each including one or more first photons; The system further comprises: a first attenuator that attenuates pulses of electromagnetic radiation to output attenuated pulses each including a first average number of first photons, the first average number of photons received on the combiner increasing a likelihood that the combiner will cause one of the first photons to interact with one of the second photons to form interference; a first filter electromagnetically coupled to the coupler and configured to spectrally filter the electromagnetic radiation to increase indistinguishability between one of the first photons and one of the second photons; one or more second filters electromagnetically coupled to the source of entangled photon pairs (including one of the second photons and one of the third photons) and configured to spectrally filter the entangled photons; Equipped with the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early and a later arriving photon; and the source of the pair of entangled photons includes a laser that excites a nonlinear material to output a second photon comprising an idler photon and a third photon comprising a signal photon according to a spontaneous parametric down-conversion (SPDC) process. A system or method.

[0024] [Example 16] In the system or method of Example 13 or 14, the benchmarking includes using a model to simulate at least one of the teleportation fidelity of the first quantum bit teleported to one of the third photons received at detector D3 or the degree of indistinguishability between one of the first photons and one of the second photons as a function of the average number of second photons, the model being calibrated and validated using experimental measurements of the teleportation fidelity and the degree of indistinguishability.

[0025] [Example 17] 17. The method of example 16, wherein the coupler comprises a beam splitter or a linear optical device capable of interfering photons or electromagnetic fields.

[0026] [Example 18] In the system or method of Example 16, the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early and a late arriving photon; the source of entangled photons includes a laser that excites the nonlinear material to output one of the second photons, including an idler photon, and one of the third photons, including a signal photon, according to a spontaneous parametric down-conversion (SPDC) process; The clock signal includes a clock cycle. The data collection system is a coincidence rate involving events in which one of the second photons and one of the third photons in the entangled photon pair are detected in the same one of the clock cycles; and a contingency rate involving events in which one of the second photons and one of the third photons in the entangled pair are detected in different clock cycles; Measure the average number of second photons by comparing The degree of indistinguishability was measured by performing the Hon-Mandel experiment, which uses a coupler containing a beam splitter to observe interference, and A system or method wherein the fidelity of the teleportation is measured using an interferometer that measures the visibility of the interference of a third photon with itself.

[0027] [Example 19] In the system or method of Example 18, The model calculates the fidelity and indistinguishability of the teleportation, and this calculation is The probability P of coincident detection of one-triple of photons in each of the detectors D1, D2 and D3 3f , i.e.

number

[0028] [Example 20] In the system or method according to Example 19,

number

[0029] [Example 21] Quantum teleportation of time-binned qubits with average fidelity F ≥ 90% at telecom wavelengths. This is achieved using a compact setup of fiber-coupled devices, including low dark count single-photon detectors and commercially available optics, allowing the reproduction of multi-node networks. To illustrate the compatibility of the network, we perform the teleportation using up to 44 km of single-mode fiber between qubit generation and measurement of the teleported qubits, facilitate it using a semi-autonomous control, monitoring and synchronization system, and collect the results using scalable collection hardware. Operating at a clock rate of at least 90 MHz, the system can be operated remotely for days without interruption, and teleportation rates of several Hertz can be obtained using the entire length of fiber. Our qubits are also compatible with erbium-doped crystals (e.g., Er:Y2SiO5), which have been used to develop quantum network devices such as memories and transducers [Refs. 48–50]. The example 1536.5-nm operating wavelength is within the low-loss (C-band) communications window for long-distance communication, and a variety of off-the-shelf equipment is available. Analytical models of our system, including experimental imperfections, predict that the fidelity can be further improved toward unity through well-understood methods (e.g., improving photon indistinguishability). [Brief description of the drawings]

[0030] Referring now to the drawings, like reference numbers represent corresponding parts throughout: [Figure 1]A schematic diagram of the quantum teleportation system including Alice, Bob, Charlie and the data acquisition (DAQ) subsystem is shown. An explanation of each subsystem is referred to the main text. One cryostat is used to house all the SNSPDs and is depicted as two cryostats for ease of explanation. The detection signals generated by each SNSPDs are labelled 1-4 and are collected by the TDC, 3 and 4 are time-division multiplexed. All individual components are labelled in the legend, the single-mode optical fibre (electronic cable) is in grey (green) and the monochromatic and bichromatic (i.e. unfiltered) light pulses are shown. [Diagram 2] is the confounding visibility. Varying the temperature of the interferometer reveals an expected sinusoidal variation in the occurrence rate of coincidence events. The fit reveals a confounding visibility Venf = 96.4 ± 0.3% (see text for details). Uncertainties here and in all measurements have been calculated assuming Poisson statistics. [Diagram 3] This is Hon-Ohmandel (HOM) interference. It introduces a relative arrival time difference between the photons from Alice and Bob at Charlie's BS. HOM interference reduces the coincidence detection rate by a factor of 3 for photons measured after Charlie's BS and at Bob's SNSPDs. Fits reveal (a) VHOM=70.9±1.9% and (b) VHOM=63.4±5.9% for additional lengths of fiber (see text for details). [Figure 4] Quantum teleportation |+〉. Teleportation is performed with (b) and without (a) the addition of 44 km of single-mode fiber to the system. Varying the temperature of the interferometer gives a sinusoidal variation of 3 times the coincidence at each output of the MZI (blue and red dots). Fitting the visibility measured at each output of the MZI (V+,1,V+,2) gives an average visibility V+=(V+,1+V+,2) / 2 of (a) 69.7±0.91% without additional fiber and (b) 58.6±5.7% with additional fiber. [Diagram 5]Quantum teleportation fidelity for |e〉A′, |l〉A, and |+〉A′ including the average fidelity. The dashed lines represent the classical bounds. The fidelity using QST is shown in blue bars, and the minimum fidelity for qubits prepared using DSM, respectively, including the associated average fidelity, is shown in grey. (a) and (b) are the results with and without the addition of fiber, respectively. The uncertainties are calculated using Monte Carlo simulations with Poisson statistics. The uncertainties without and with the fiber spool are similar to those used for QST in μA, thus agreeing with previous measurements. [Figure 6] Schematic of distinguishability between Alice's and Bob's photons at Charlie's BS. Distinguishability is modeled by a virtual BS with transmittance ζ. Indistinguishable photons contribute to interference at Charlie's BS, while distinguishable photons mix with the vacuum, reducing the visibility of the HOM and the fidelity of teleportation (see text for details). [Figure 7] Evaluation of photon indistinguishability using the analytical model. (a) Fidelity of quantum teleportation of |+). (b) Visibility of HOM interference by varying the average number of photons μA of Alice's qubit. Fitting the analytical model to the data, we find that at Charlie's BS, Alice's and Bob's photons are indistinguishable ζ=90% of the time. Bob produces on average photon pairs μB, while ηi and ηs are the probabilities, respectively, of an individual idler (signal) photon arriving at Charlie's BS and being detected by Bob's detector. [Figure 8] The elements of the density matrix for the teleported |e〉, |1〉 and |+〉 states and the addition of 44 km of fiber into the system. The black dots are generated by our teleportation system, while the blue bars and dashed red line are the values ​​assuming ideal teleportation. [Figure 9] Density matrix elements of the teleported |e〉, |{〉, and |+〉 states. The black dots are generated by our teleportation system, while the blue bars and dashed red lines are assuming ideal teleportation. [Figure 10]1 is an example of a hardware and software environment. [Figure 11] 1 illustrates a schematic diagram of a typical distributed / cloud-based computer system in which client and server computers are connected via a network.

[0031] Explanation of [Figure 5] JPEG2025506324000006.jpg61166 DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0032] In the following description of the preferred embodiment, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention.

[0033] (Technical explanation) (1. Example of a teleportation system) 1 summarizes a quantum teleportation system 100 that implements a teleportation protocol in which a photonic qubit (provided by Alice) interferes with one member of an entangled photon pair (from Bob) and is projected into a Bell state (by Charlie), such that the state of Alice's qubit can be transferred to the remaining member of Bob's entangled photon pair. Photons are transmitted using a single-mode fiber, all qubits are generated at a clock rate, and all measurements are collected using a data acquisition (DAQ) system.

[0034] FIG. 1 illustrates a quantum teleportation system 100 including a transmitter 102 that generates a first photon 104 (carrying a first quantum bit), a source 106 of respective pairs 108 of entangled photons including a second photon 110 entangled with a third photon 112 (carrying a second quantum bit), a receiver 114 that is electromagnetically coupled to the transmitter and the source of the entangled photon pairs, and a detection system 118 that includes a pair of detectors D1 and D2 electromagnetically coupled to the coupler, and a detector D3 that detects the third photon 112. The system includes a receiver 116, an optical fiber 120 connecting a source of the entangled photon pair with a detector D3, which detects a third photon transmitted along the optical fiber, a clock distribution system 122 outputting one or more clock signals 124 that control the timing of the first, second, and third photons, a data collection system 126 that acquires the arrival times of the photons, and a computer 128 that uses the arrival times to benchmark the quantum teleportation system in real time. A display 130 can display the benchmark. In one or more examples, the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early photon 140 and a late arriving photon 142.

[0035] Each subsystem is described in more detail in the following subsections.

[0036] (a. Alice: Creation of a single quantum bit) To generate the time-bin qubits that Alice teleports to Bob, light from a fiber-coupled, telecom-wavelength (e.g., 1536.5 nm) continuous wave (cw) laser is input to an intensity modulator (IM). In this example, the IM is a lithium niobate intensity modulator. The IM is driven with one pulse or two pulses separated in time (e.g., separated in time by less than 10 ns, .2 ns in this example). Each pulse has a full width at half maximum (FWHM) duration of approximately 100 ps or less (65 ps in this case). The pulses are produced with an arbitrary-waveform generator (AWG) and amplified with a high-bandwidth amplifier to produce optical pulses with an extinction ratio of 1.2 dB. In this example, the amplifier has a gain of 27 dB and an extinction ratio of up to 22 dB. Note that this method of creating time-bin qubits offers flexibility not only in choosing the appropriate time-bin separation, but also in synchronizing qubits originating from different nodes in the network. A polarization-maintaining beam splitter (BS) combined with a power monitor (PWM) is used to apply feedback to the dc bias port of the IM to keep the extinction ratio constant (e.g., 22 dB) [Ref. 54]. In this example, the BS is a polarization-maintaining fiber BS that maintains at least 90% polarization (90:10 polarization-maintaining fiber BS). For the quantum teleportation protocol to run successfully, the photons from Alice and Bob must be indistinguishable in all degrees of freedom. Therefore, the light pulses at the output of the IM are bandpass filtered with a filter 132 (see Fig. 1), for example using a fiber Bragg grating (FBG), to match the spectrum of the photons from the intertwined source (Bob). In this example, the FBG bandwidth has a 2 GHz bandwidth (FWHM) centered on the wavelength of the photons (1536.5 nm in this case).Furthermore, the polarization of Alice's photons is determined by a manual polarization controller (POC) in conjunction with Charlie's polarizing beam splitter (PBS). Finally, the light pulse from Alice is attenuated to the single-photon level by an attenuator (134 in Fig. 1, e.g., a variable optical attenuator (VOA)).

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[0037] (b. Bob: Entangled qubit generation and teleport qubit measurement) Similar to Alice, one (two) telecom wavelength optical pulses with the same wavelength as Alice's pulses and FWHM (e.g., less than 100 ps) are created using an IM and a CW laser driven by an AWG, BS and PWM. In this example, the optical pulse wavelength is 1536.5 nm, the optical pulse FWHM is about 65 ps, the pulses are spaced 2 ns apart, the IM is a lithium niobate IM, the BS is a 90:10 BS, and the PWM maintains an extinction ratio of at least 20 dB. An amplifier (in this example, an erbium-doped fiber amplifier (EDFA)) is used after the IM to boost the pulse power and maintain a high output rate of photon pairs.

[0038] In this example, the output of the EDFA is sent into a type-0 periodically poled lithium niobate (PPLN) waveguide for second harmonic generation (SHG) to upconvert the pulses to 768.25 nm. Residual light at 1536.5 nm is removed by a bandpass filter with an extinction ratio of ≥ 80 dB. These pulses undergo spontaneous parametric downconversion (SPDC) using a type-II PPLN waveguide coupled to a polarization-maintaining fiber (PMF), producing photon pairs |pair〉 when one or two pulses are used to drive the IM, respectively. B =|ee〉 B or time bin confounding condition

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[0039] The order of states refers to a pair of so-called signal and idler modes, the former with polarization parallel and the latter orthogonal to the axis of the PMF. As mentioned above, the relative phase is |ll〉 B Each photon is separated into a different fiber using a PBS and spectrally filtered with FBGs similar to those used by Alice. Note that the bandwidth of the FBGs is chosen as a trade-off between spectral purity and the generation rate of Bob’s photons

[55] .

[0040] The idler mode photons are sent to Charlie for teleportation or HOM measurements, or to a Mach-Zehnder interferometer (MZI) for characterization of the entangled state, and their polarization is determined using a POC (for example). The signal mode photons are sent to the MZI via the POC (and, in one or more examples, 11 km of single-mode fiber for some measurements) and detected by a low dark count single-photon detector. In the example shown here, the single-photon detectors include superconducting nanowire single-photon detectors (SNSPDs) [Ref. 56] after high-pass filtering (HPF) to remove any remaining 768.25 nm light. The MZI and detectors are used for projection measurements of the teleported state, characterization of the time-bin entangled state, or measurement of the HOM interference at Charlie. The photon arrival times are recorded by the DAQ subsystem using a time-to-digital converter (TDC) referenced to the clock signal from the AWG.

[0041] All SNSPDs are mounted in a compact adsorption refrigerator cryostat [Ref. 57] and are operated at a temperature of 0.8 K, typically for 24 h, before a 2-h downtime is required. Our SNSPDs have been developed by the applicant and have detection efficiencies between 76 and 85% at low dark count rates of 2-3 Hz. The FWHM time resolution of all detectors is between 60 and 90 ps, ​​with a recovery time of about 50 ns.

[0042] The MZI has a path length difference equal to the time separation of the time bin photons (2 ns in this case) and detects photons with three different arrival times at one of its outputs and, by varying the relative phase φ, B’ , |l〉 B’ and (|e〉 B +e iφ |l〉 B) / √2 projection measurement [Reference 32]. Detection at the other output gives the same measurement, except when the relative phase is φ+π. In one or more embodiments, a custom temperature feedback system is used to slowly vary the temperature over a time interval of up to 15 h, within the hold time of the cryostat, to collect all measurements.

[0043] (c. Charlie: Bell State Measurement) Charlie consists of a 50:50 polarization-maintaining fiber BS, where the relevant photons from the Alice and Bob subsystems are directed to each input via the PBSs and optical fibers. After the HPFs, the photons are detected at each output by single-photon detectors (SNSPDs) and the arrival time is recorded using a DAQ, as was done with Bob. Teleportation is

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[58] . 2 〉 AB The projection onto the state corresponds to the teleportation of |A〉 up to a known local unitary transformation. That is, our system is −iσ y |A〉, where σ y is the Pauli y matrix.

[0044] (d. Control Systems and Data Acquisition) Our system is built with a view to future replicability, with a particular focus on system integration. Each subsystem, Alice, Bob and Charlie, is equipped with monitoring and active feedback stabilization systems (e.g., IM extinction ratio) or remote control of key network parameters (e.g., varying the generation time of qubits). Each subsystem has a central classical processing unit whose functions include monitoring the automated functions and workflows within the subsystem, collecting and managing data, and handling input and output synchronous streams. Since quantum information is encoded in the time domain, the correct operation of the classical processing unit crucially depends on recording the arrival times of photons at the SNSPDs. Therefore, a great deal of effort has been put into building a robust DAQ subsystem capable of recording and processing at high speed the large amount of time-tagged signals generated by the SNSPDs and recorded by the TDCs. The DAQ is designed to enable both real-time data analysis for rapid data quality monitoring and post-processing data analysis to enable the best understanding of the data.

[0045] In the example presented here, the DAQ system is built on a standalone Linux library of a commercially available TDC. It records a time tag whenever a signal coinciding with a reference (90 MHz in this example) clock is detected on any channel. The time tags are streamed to a computer where they are processed in real time and stored on disk for future analysis. A graphical user interface is developed, allowing real-time visualization and monitoring of detected photons during teleportation runs. It also allows easy control of the time interval used for each channel and configuration of associated coincidences between different photon detection events across all TDC channels. We expect this DAQ subsystem to serve as a foundation for future real-world time-binned quantum networking experiments and applications (see Section 8).

[0046] (e. Example of a single-photon detector with low dark counts: Superconducting nanowire single-photon detector) In the example presented here, the low dark count single photon detectors include amorphous tungsten silicide SNSPDs fabricated at the JPL Microdevices Laboratory for all measurements at the single photon level [Ref. 56]. The entire detection system is customized for optimal autonomous operation within the quantum network. The SNSPDs are operated in a closed cycle sorption refrigerator. The detector nanowire widths are between 140 and 160 nm and biased with a current of 8–9 μA. The FWHM timing jitter (i.e., time resolution) of the entire detector is between 60 and 90 ps (measured using a Becker & Hickl SPC-150NXX time tagging module). The detection efficiency of the system (measured from the fiber bulkhead of the cryostat) is between 76 and 85%. SNSPDs are characterized by a 3-cm diameter optical fiber coil in a 40K cryogenic environment and a bandpass filter coating on the detector fiber pigtail to short-pass filter background blackbody radiation, achieving low dark count rates of 2-23% (Andover). Biasing of the SNSPDs is facilitated by cryogenic bias tees with inductive shunts to prevent latching, allowing uninterrupted operation. The detector signal is amplified at room temperature using Mini-Circuits ZX60-P103LN+ and ZFL-1000LN+ amplifiers, achieving a noise figure of 0.61 dB and a total gain of 39 dB at 1 GHz, allowing low system jitter. It is noted that in this system, the FWHM jitter can be reduced to 45 ps by biasing the detector with approximately 10 μA, at the expense of a 30 cps increase in DCR. Using commercially available components, the system is easily scalable to 64 channels per cryostat, making it ideal for star quantum networks and allowing uninterrupted 24 / 7 operation. The bulkiest component in the current system is the external helium compressor, although compact rack-mounted versions are readily available

[57] .

[0047] (f. Examples of Interferometers and Phase Stabilization) The example presented here uses the commercially available Kylia04906-MINT MZI, which is composed of free-space devices (e.g., mirrors and BSs) and has a small form factor that fits into a handheld box. Light is input and output to the MZI using polarization-maintaining fiber, with a loss of about 2.5 dB. The interferometer features an average field of view of 98.5% and has a |+〉μ A = 0.07 and measure the visibility of the fringes of each output using SNSPDs. The relative phase φ is controlled by a voltage-driven heater that induces a small refractive index change in one arm of the MZI. However, this built-in heater does not provide sufficient phase stability to measure teleportation with high fidelity, and the relative phase tracks the slowly changing ambient temperature of the room. To mitigate this instability, we build a separate enclosure that thermally isolates the MZI enclosure from the laboratory environment and controls the temperature via a closed-loop feedback control system based on a commercial thermoelectric cooler and an LTC1923 PID controller. Temperature feedback is provided by a 10-kΩ NTC thermistor, and the set point is applied by a programmable power supply. This control system allows us to measure the visibility while slowly varying φ on time scales up to 15 hours. Table 1. Sources of Bob's photon pairs and the measured average photon count μ per time bin B and characterized by true coincidence detection at various EDFA currents.

[0048] [Table 1]

[0049] (2. Characteristics of an example quantum teleportation system) We measured several key parameters of the system that underpin the fidelity of teleportation. Specifically, the visibility of entanglements, V entWe determine the fidelity of the entangled state produced by Bob by measuring [Ref. 59], and also determine the extent to which Alice's and Bob's photons are indistinguishable in Charlie's BS using the HOM effect [Ref. 51].

[0050] (a. Visibility of Confounding) The state |pair〉 described in section 1b above. B (Hence, the confounded state |φ + 〉 B ) is an idealization. In reality, the state produced by Bob is a two-mode squeezed vacuum state after the FBG filter, ignoring losses.

number

[60] , where n is the number of photons per time mode (or qubit), p is the emission probability of a single pair per mode (or qubit), and the state ordering refers to the signal and idler modes. However, |TMSV〉 B approximates photon pairs for p ≪ 1, and the average number of photon pairs per mode (or qubit) is p ≒ μ B and conditional on pair measurements such that the n=0 term is eliminated. As a compromise between pair creation rate ∝p and confounding quality, we will here and in the future define the average number of photons from the paired sources as μ B =(8.0±0.4)×10 ―3 This is feasible due to the very low dark count of SNSPDs. B The method for measuring is described in the following section.

[0051] With a slight modification to the setup in Figure 1, |φ + 〉 B and directing the idler photons to the second input port of the MZI, V entBecause the idler photons are delayed relative to the signal, we can measure each qubit unambiguously. By varying φ and accumulating coincidence events of photons at both outputs of the interferometer, we project each qubit into a phase-shifted superposition of |e〉 and |l〉 in the entangled state

[59] .

[0052] The results shown in Figure 2 are: ent sin(ωT+Φ), where V ent =(R x -R n ) / (R x +R n ) and R x(n) denotes the maximum (minimum) rate of coincidence events

[59] , ω and Φ are unconstrained constants, T is the temperature of the MZI, and V ent = 96.4 ± 0.3%.

[0053] The deviation from unit visibility is mainly due to nonzero multiphoton emission [Ref. 61], which is supported by an analytical model that includes experimental imperfections [Ref. 62]. Nevertheless, this visibility far exceeds the one-third required for the constraints on nonseparability of Werner states [Ref. 63] and locality of 1 / √2 [Refs. 59, 64]. Moreover, |φ + 〉[Reference 63] predicts fidelity F = (3V + 1) / 4 = 97.3 ± .2%, which is sufficient for quantum teleportation.

[0054] (b. Visibility of HOM interference) The BSM relies on quantum interference of photons from Alice and Bob. This is ensured by Charlie's BS, which precisely controls the arrival times of the photons using IMs, identical FBG filters and POCs (with PBSs) to provide the required indistinguishability. The degree of interference is measured by the HOM interference visibility V = (R d -R i ) / R d It is quantified by R d(i)denotes the coincidence detection rate of photons after BS when the photons are rendered as distinguishable (indistinguishable) as possible

[51] . A completely indistinguishable single photon from Alice and Bob is V HOM = 1. However, in our system, Alice's qubit is in a coherent state

number

[60] . Thus, the contribution of unwanted photons from Alice and Bob is the maximum achievable V HOM below unity, and even lower if the interfering photons are completely indistinguishable. A and μ B V for changes in HOM The dependence on is analytically modeled in

[62] and is further detailed in Section 5 below.

[0055] With a slight modification to the setup in Figure 1, HOM Measure |A〉=|e〉 A μ A =2.6×10 -3 and Bob is |pair〉 B As a result, Alice’s photons and Bob’s idler are directed to Charlie, and Bob’s signal is directly measured by the SNSPD, bypassing the MZI. The IM of Alice is the relative arrival time difference Δt between Alice’s and Bob’s photons at Charlie’s BS. AB Using Charlie's SNSPDs and Bob's third detector, Δt AB We measured a three-fold increase in coincidence detection rate when varying , and the results are shown in Figure 3(a). Since the photon time profile is approximately Gaussian, the results are

number

[0056] To test quantum teleportation over long distances, we introduced single-mode fibers with lengths of 22 km, 11 km, and 11 km between Alice and Charlie, between Bob and Charlie, and on the path of Bob's signal photon, respectively, and measured V HOM The measurements were repeated and the results were fitted as before [see Figure 3(b)]. HOM = 63.4 ± 5.9%, which is the maximum V expected when including the effects of the 5.92-(2.56-) dB loss between Charlie and Alice (Bob) and photon discrimination (analyzed in Section 4). HOM This importantly suggests that the added fiber does not introduce any further distinguishability (that we cannot take into account), thereby supporting our system for use in quantum networking. Overall, the presence of clear HOM interference suggests that our system (with or without the additional fiber) introduces relatively few imperfections that would adversely affect the fidelity of the BSM and quantum teleportation.

[0057] (13. Quantum teleportation using the example quantum teleportation system) We perform quantum teleportation of the time-bin qubit's basis states |e〉, |l〉, and |+〉 and measure the teleportation fidelity F e , F iand F+ up to the local unitary introduced by the BSM, respectively, for the ideal corresponding states (see section 1c). The measurement by the symmetry of |+〉 in our setup is (|e〉+e iφ Since this is equivalent to any state of |e〉−|l〉 / √2 (and in particular the remaining three basis states (|e〉−|l〉) / √2 and (|e〉±i|l〉) / √2), the average teleportation fidelity of any time bin qubit F avg =(F e +F l +4F + ) / 6 can be determined.

[0058] First, μ A =3.53×10 -2 |e A 〉 and |l〉 A So that Bob's idler can be detected by one SNSPD, bypassing the MZI. e = 95 ± 1%, F l =96±1%. This is Charlie |Ψ - 〉 AB Provided that we successfully measure μ, the fidelity is limited by the multiphoton events of the Alice and Bob qubits and the dark counts of the SNSPDs

[62] . Then, μ A =9.5×10 -3 Then, to emulate a large distance separating some of Alice, Charlie, and Bob, we repeat the measurement after inserting a length of fiber as described above (in this example, 44 km of fiber length). This results in F e = 98 ± 1%, F l = 98 ± 2%, and there is no degradation due to additional fiber loss due to low noise single photon detectors (SNSPDs). Next, μ A =9.38×10 -3 |+〉 A Prepare the antenna, insert the MZI, and change φ under the condition of BSM. + =(1+V + ) / 2=84.9±0.5%, where V += 69.7 ± 0.9% is the average visibility obtained by fitting to the measured interference results at each output of the MZI, as shown in Fig. 4(a). The decrease in fidelity from unity is due to multiphoton events and discernibility, as supported by further measurements and analytical modeling in section 5, and is consistent with that inferred from HOM interference.

[0059] Repeating the measurement with a longer fiber length increases V + = 58.6 ± 5.7%, F + = 79.3 ± 2.9%, and the results and the corresponding fit are shown in Fig. 4(b). The degradation in fidelity can be attributed to the aforementioned polarization variations over the long fiber, which coincide with the reduced visibility of the HOM interference, and is exacerbated here due to the non-ideal visibility of the MZI over the long measurement time.

[0060] The results are F without (and with) additional fiber. avg = 89 ± 1% (86 ± 3%), which is significantly higher than the classical 2 / 3 limit and represents strong evidence for quantum teleportation

[66] . It is also limited from unity by multiphoton events, distinguishability and changes in polarization, as mentioned above

[62] .

[0061] To gather more information about our teleportation system beyond fidelity, we reconstruct the density matrix of the teleported states using maximum likelihood QST [Ref. 52], described in Section 7. The QST results with and without the additional fiber length are summarized in Figs. 8 and 9, respectively. As can be seen, the diagonal elements of |+〉 are very close to the expected values, indicating that the ground state probabilities of |e〉 and |l〉 after teleportation are preserved, while the deviations of the off-diagonal elements indicate a degradation of the coherence between the ground states. Decoherence is due to the fact that |+〉 AConsistent with the previously mentioned teleportation fidelity of F due to the multiphoton emission and distinguishability from our entangled pair sources, which is further detailed in Section 5. Finally, we also extract the teleportation fidelity from these density matrices, and compare the results shown in Fig. 5 with those of F without and with the fiber spool. avg = 89 ± 1% (88 ± 3%), which is similar to the μ A Considering this, it is consistent with previous measurements.

[0062] Using weak coherent states instead of ideal single photons reduces the fidelity of teleportation due to multiphoton events; we discuss this effect further in Section 5. We also point out that the 2 / 3 classical bound only applies if Alice prepares her qubit with a true single photon, i.e., |n=1〉, rather than using |α≪1〉 as we did in this work

[67] . We move on to an analysis using decoy states as a way to describe the photon statistics of Alice's qubit.

[0063] (3. Fidelity of Teleportation Using Decoy States) To determine the minimal teleportation fidelity of a qubit prepared using a single photon, we use the DSM

[53] and follow the approach of [33, 68]. Decoy states, traditionally used in quantum key distribution to defend against photon number splitting attacks, are A = |α| 2 The quantum bit is encoded in a coherent state |α〉 by A By measuring the fidelity of the teleported qubit to |n=1〉, the DSM can determine the fidelity of the teleportation if Alice encoded the qubit using |n=1〉. JPEG2025506324000014.jpg713 can be calculated.

[0064] JPEG2025506324000015.jpg73166

[0065] In Table 2, μ A The fidelity of teleportation with (right column) and without (middle column) a 44-km-long fiber for Alice’s qubit states prepared by varying . We assume that the average photon number and fidelity in the vacuum state with the fiber are zero and 50%, respectively.

[0066] [Table 2]

[0067] (4. Analysis model and simulation example) As suggested by our measurements, the multiphoton component of Alice’s and Bob’s qubits and the indistinguishability between them degrades the values ​​of key metrics, including the visibility of HOM interference, and consequently the fidelity of quantum teleportation. To capture these effects in our model, we employ the Gaussian state characteristic function method developed in

[62] , which was made possible by the work in

[71] . This method is well suited to the analysis of our system, since it allows the quantum states, behaviors, and experimental imperfections (including losses, dark counts, etc.) to be fully described using Gaussian operators (see, for example,

[72] ). Here, we briefly outline the model in

[62] and use it to estimate the amount of indistinguishability ζ between Alice’s and Bob’s qubits in the measurements of HOM interference and quantum teleportation.

[0068] Distinguishability at any degree of freedom can be modeled by introducing a hypothetical BS with transmittance ζ into the paths of the relevant photons from Alice and Bob. As shown in Figure 6, the indistinguishable components of the incoming photon modes are directed to Charlie's BS and interfere there, while the distinguishable components mix with the vacuum at the BS and do not contribute to the interference. Here, ζ=1 (ζ=0) corresponds to the case where both incoming photons are completely indistinguishable (distinguishable). Now, for a given qubit state ρ from Alice and Bob, ABFor D1, D2 (Charlie's detectors) and D3 (detecting Bob's signal photon), the probability P 3f can be calculated.

number

number

[0069] To compare the model with measurements, we determined the experimental mean photon number η of the photon pair source as described in Appendix B. i =1.2×10 -2 and η s =4.5×10 -3 Next, we use various values ​​of μ A For |+〉 teleportation fidelity and HOM interference visibility (η s The data is then compared to the model-derived equation V HOM We fit F(ζ) and F(ζ) to the approximation F(ζ) and plot them in Figure 7. The maximum teleportation fidelity and HOM visibility are about 0.85 and 0.65, respectively, and μ A = 0.001. A When μ = 0, the teleportation fidelity and HOM visibility are reduced to 0.5 and 0.0, respectively, which corresponds to a vacuum input from Alice. A The decrease at large values ​​of is mainly due to multiphoton events from Alice.

[0070] The fitted curves matched the experimental values ​​very well, yielding a consistent value of ζ=90% for both types of measurements. This means that there remains a small degree of distinguishability between Alice's and Bob's photons. We will discuss the potential effects that lead to this distinguishability in more detail in Section 8.

[0071] Overall, our analytical model is consistent with the experimental data

[62] and, in our experimental setup, we find that μ A High-fidelity teleportation of any time-bin qubit is possible in the regime ≪ 1. Our model thus provides a practical way to determine the fundamental distinguishability in deployed networks where it may not be possible to fully characterize the properties of Alice's and Bob's photons.

[0072] (5. Estimation of the average number of photon pairs and the transmission efficiency of signal and idler photons Using the method described in

[59] , we find the average number of photon pairs produced by Bob, μ B as a function of the laser pump power in front of the PPLN waveguide used for SHG. For this, we modify the setup of Fig. 1 and direct each of Bob's signal and idler photons into the SNSPD. We then measure the detection events while varying the amplification of the EDFA by the applied current. We extract events when pairs of photons originating from the same clock cycle are measured in coincidence and when a photon originating from one cycle is measured in coincidence with a photon originating from the previous or next clock cycle. In other words, we measure the so-called coincidence and coincidence rates. The ratio of the coincidence rate and the coincidence rate is μ B ≪1 and all results are shown in Table 2. For all measurements, μ B =(8.0±0.4)×10 -3 It supports EDFA current of 600mA.

[0073] The transmission efficiency η of the signal and idler photons mentioned in Section 5 s and η iis determined by calculating the ratio of the independent detection rates of the idler and signal photons to the coincidence rate of pairs of photons (within the same clock cycle) [Ref. 59]. We repeated the measurement using the setup shown in Fig. 1, which was used to generate the results in Fig. 7 (i.e., directing the signal and idler photons into the setup as if to perform teleportation). η s =4.5×10 -3 , η i =1.2×10 -2 It was found that the loss between the time the photons are generated and the time they are detected by the respective low-dark-count single-photon detectors (SNSPDs) was taken into account.

[0074] (6. Quantum State Tomography) We consider the Pauli matrix σ x , σ y and σ z In all three qubit bases formed by A , |l〉 B , |+〉 A We perform projective measurements of the state, i.e., we measure photons at each arrival time after the MZI and at various φ. From these results, we can use maximum likelihood estimation

[52] to reconstruct the density matrix of each teleported state, both with and without the addition of fiber (e.g., 44 km). The resulting matrices unambiguously match the expected teleported states, with the high teleportation fidelity calculated in section 3, up to the effects of multiple photons and distinguishability mentioned above.

[0075] (7. Advantages and Improvements) The exemplary results and systems presented herein demonstrate a quantum teleportation system of photonic time-bin qubits at quantum channel and device compatible wavelengths of 1536.5 nm using a fiber-based setup including state-of-the-art SNSPDs and commercially available components. With this setup, we measured average fidelity of over 90% using QST and decoy state analysis over up to 44 km of single-mode fiber. Our results are further supported by analytical models coupled with measurements of entanglement and HOM interference visibility.

[0076] From the analysis of decoy states, the maximum teleportation fidelity is currently limited to that of teleported qubits prepared in a superposition state, with a 10% distinguishability between qubits undergoing BSM and the contribution of multiple photon pairs playing the largest role. Our model predicts that the average fidelity rises to 95% for completely indistinguishable photons, while fidelity close to unity can be achieved for a smaller number of average photon pairs. Alternatively, one could consider replacing SNSPDs with efficient photon-number-resolving (PNR) SNSPDs

[73] , allowing post-selection of multiphoton events with MZIs or BSMs

[74] . Both approaches require an increase in the coupling efficiency of the pair sources beyond the current ~1% to maintain a realistic teleportation rate (above the system noise and the current phase drift rate of the MZI) or to derive any benefit from the PNR feature.

[0077] As suggested by the width of the HOM fringes, the average photon bandwidth is predicted to be 0.44 / σ~1.5 GHz (see section 2b), i.e. smaller than the 2 GHz bandwidth of the FBGs. Indistinguishability in the system may be limited by the large difference in bandwidth between the photons generated by the SPDC (>100 GHz) and those generated at Alice by the IM (15 GHz), leading to non-identical filtering by the FBGs. This can be improved by narrowing the width of the FBGs or using a broader pump at Alice [e.g., using a mode-locked laser or a commercially available broader IM (e.g., >50 GHz)]. Alternatively, pure photon pairs can be generated by designing phase matching (see, e.g., ref.

[75] ).

[0078] Distinguishing properties due to nonlinear modulation during the SHG process may also play a role

[76] . Whether due to imperfect filtering or other device imperfections (e.g., PBS or BS), the source of distinguishability in our system can be studied. Coupling losses can be minimized to less than a few decibels overall by improved fiber-to-chip coupling, low-loss components in the FBGs (e.g., the required isolators), spliced ​​fiber connections, and reduced losses in the MZI. We note that the current coupling efficiency is equivalent to about 50 km of single-mode fiber, suggesting that this system would be suitable for quantum networks if losses were reduced.

[0079] The fidelity we have demonstrated is sufficient for some applications, and the current teleportation rate with a 44 km fiber length is in the approximate Hertz range, but this can be improved. Higher repetition rates (e.g., using high-bandwidth modulators with wideband wavelength division multiplexing filters and low-jitter SNSPDs

[77] ), improved coupling and detector efficiency, improved BSM efficiency with fast-recovery SNSPDs

[78] or frequency multiplexing

[68] all lead to significant increases in the teleportation rate to gigahertz levels. It is noted that the increased repetition rate allows for a lower time-bin separation, so that MZIs can be built on chip, providing outstanding phase stability and achievable fidelity. Importantly, improvements in low-dark-count single-photon detector (e.g. SNSPD) technology will further provide the aforementioned improvements in repetition rate and efficiency.

[0080] Further system-level improvements include further automation through the implementation of free-running temporal and polarization feedback schemes to render photons indistinguishable in the BSM [Refs. 33, 34]. Furthermore, some electrical components can be miniaturized, scaled, and made cost-effective (e.g., a field-programmable gate array could replace the AWG). We note that our system can be extended to independent lasers at different locations with appropriate feedback mechanisms for spectral overlap [Refs. 79, 80]. These modifications are compatible with the data acquisition and control system.

[0081] Overall, a high-fidelity teleportation system that achieves state-of-the-art teleportation fidelity for time-bin qubits serves as a blueprint for the construction of quantum network testbeds and, ultimately, a global quantum network towards a quantum internet. In this disclosure, we describe a full analytical model of the teleportation system, including imperfections, and compare it to our measurements. Our implementation, using approaches from the HEP experimental system and real-world quantum networks, features nearly fully automated data collection, monitoring, and real-time data analysis. The high fidelity achieved in our experiments using practical, replicable devices will be essential when scaling quantum networks to large numbers of nodes, enabling the realization of more advanced protocols (see, e.g., refs. [18, 81, 82]).

[0082] (Device embodiment) The devices, systems, quantum teleportation systems and methods of operating teleportation systems can be embodied in many ways, including but not limited to the following (see also reference numerals in Figures 1-11).

[0083] [Example 1] A quantum teleportation system (100), comprising: A transmitter (102) that generates a first photon (104); a source (106) of pairs (108) of entangled photons, each pair (108) including a second photon (110) entangled with a third photon (112); a coupler (114) electromagnetically coupled to the transmitter (102) and to the source (106) of entangled photon pairs (108); a pair of detectors D1 and D2 electromagnetically coupled to a coupler (114); a receiver (116) including a detection system (118) having a detector D3 for detecting the third photon (112); an optical fiber (120) connecting a detector D3 and the source (106) of the pair of entangled photons (108), the detector D3 detecting a third photon (112) transmitted along the optical fiber (120); a clock distribution system (122) that outputs one or more clock signals (124) that control the timing of the first photon (104), the second photon (110), and the third photon (112); a coupler (114) for causing one of the first photons (104) carrying the first quantum bit (60) and one of the second photons (110) carrying the second quantum bit to interact with each other to form interference; a pair of detectors D1 and D2 detect interference used to obtain a Bell state measurement of a quantum system including a first qubit and a second qubit; Detector D3 detects one of the third photons (112) intertwined with one of the second photons (110) and outputs a signal in response thereto; and A detection system (118) reads the state of the first qubit using the signal and the Bell state measurement. a clock distribution system that outputs the clock signal (124); a data collection system (126) that collects arrival times of the first photon (104) and the second photon (110) at detectors D1 and D2 and the arrival time of the third photon (112) at detector D3, where the arrival times are tagged with reference to a clock signal (124) such that one or more photons are identified into sets, each set including one of the first photons (104), one of the second photons (110), and one of the third photons (112); and a computer (128, 1000, 1002) (e.g., a classical computer, e.g., a non-quantum computer) that benchmarks the quantum teleportation system (100) in real time using arrival times; A system comprising:

[0084] [Example 2] In the system (100) described in Example 1, A transmitter (102) generates pulses of electromagnetic radiation (103), each pulse including one or more first photons (104); The system (100) further comprises: a first attenuator (134) that attenuates the pulses of electromagnetic radiation to output attenuated pulses each including a first average number of first photons (104), the first average number of photons received at the combiner (114) increasing the likelihood that the combiner (114) will cause one of the first photons (104) to interact with one of the second photons (110) to form interference; a first filter (132) electromagnetically coupled to the combiner (114) and configured to spectrally filter the electromagnetic radiation to increase indistinguishability between one of the first photons (104) and one of the second photons (110); one or more second filters electromagnetically coupled to the source (106) of entangled photon pairs (108) for spectrally filtering the entangled photons; Equipped with The first qubit and the second qubit each include a time bin qubit that includes a superposition of an early arriving photon (140) and a late arriving photon (142); and the source (106) of entangled photon pairs includes a laser (LAS) that excites a nonlinear material (107) to output the second photons (110) comprising idler photons and the third photons (112) comprising signal photons according to a spontaneous parametric down-conversion (SPDC) process; It is a system.

[0085] [Example 3] In the system described in Example 1 or 2, the benchmarking includes determining at least one of the following: a fidelity of teleportation of the first quantum bit teleported to one of the third photons (112) received at D3, a degree of indistinguishability between one of the first photons (104) and one of the second photons (110), or a three-fold coincident photon detection rate of one of the photons (104), (110), (112) detected in coincidence at each of D1, D2, and D2 of the system.

[0086] [Example 4] In a system described in any of Examples 1 to 3, the benchmarking includes using a model or algorithm to simulate at least one of the teleportation fidelity of the first quantum bit teleported to one of the third photons (112) received at detector D3, or the degree of indistinguishability between one of the first photons (104) and one of the second photons (110) as a function of the average number of second photons (110), the model being calibrated and validated using experimental measurements of the teleportation fidelity and the degree of indistinguishability.

[0087] [Example 5] In the system according to any one of the first to fourth embodiments, the first qubit (60) and the second qubit (60) each include a time bin qubit that includes a superposition of an early arriving photon (140) and a later arriving photon (142); the source of entangled photons (106) includes a laser (LAS) that excites the nonlinear material (107) to output one of the second photons (110), which includes an idler photon, and one of the third photons (112), which includes a signal photon, according to a spontaneous parametric down-conversion (SPDC) process; The clock signal (124) includes clock cycles (125); The data acquisition system (126) measures the average number of second photons (110) by comparing: a coincidence rate involving an event in which one of the second photons (110) and one of the third photons (112) are detected in the same one of the clock cycles (125); and a contingency rate that includes an event in which one of the second photons (110) and one of the third photons (112) in the entangled photon pair (108) are detected in different clock cycles; Measure the average number of second photons (110) by comparing It is a system.

[0088] [Example 6] The degree of indistinguishability in the system described in either Example 4 or 5 is measured by performing a Houmandell experiment to observe interference using a combiner (114) including a beam splitter (BS); and The fidelity of the teleportation is measured using an interferometer (MZI) that measures the visibility of the interference of the third photon (112) with itself in the system.

[0089] [Example 7] In the system according to any one of the fourth to sixth embodiments, the model calculates the fidelity of the teleportation and the amount of indistinguishability, and the calculation is The probability P of coincident detection of one-triple of photons in each of the detectors D1, D2 and D3 3f , i.e.

number

[0090] [Example 8] In the system described in Example 7,

number

[0091] [Example 9] In the system according to any one of Examples 1 to 8, the first qubit comprises a first time bin qubit, the second qubit comprises a second time bin qubit; The clock signal (124) includes clock cycles (125); The data collection system (126) a coincidence rate, which includes events in which one of the second photons (110) and one of the third photons (112) in a pair of entangled photons (108) are detected in the same one of the clock cycles (125); and a contingency rate that includes an event in which one of the second photons (110) and one of the third photons (112) in the entangled photon pair are detected in different clock cycles; a first detection rate of the second photons (110); and a second detection rate of the third photon (112); and Get η i is the second detection rate divided by the concordance rate, and η s is the first detection rate divided by the match rate, and The average number of second photons (110) per time bin is the chance rate divided by the coincidence rate for the system.

[0092] [Example 10] In any of the systems described in Examples 4 to 9, the model calculates the probability that detectors D1, D2 and D3 receive a first photon (142), a second photon (110) and a third photon (112) in the same clock cycle (125) using fitting parameters including transmittances representing indistinguishable quantities.

[0093] [Example 11] In a system described in any of Examples 1 to 10, the computer (128) uses the benchmark to output feedback used to optimize at least one of the timing, intensity of the entangled photons (108) output from the source of entangled photons (106), spectral filtering of the photons, or attenuation of the pulse of electromagnetic radiation so as to achieve a teleportation fidelity of greater than 0.90 or 0.99 (99%) when the third photon (112) travels a distance of at least 22 kilometers along the optical fiber (120).

[0094] [Example 12] The system of any one of Examples 1 to 10, further comprising a display (130) for displaying benchmarks (e.g., graphically displaying benchmarks such as teleportation fidelity, indistinguishability, etc., so that the benchmarks can be visualized, e.g., on a plot).

[0095] [Example 13] 1. A method of teleporting using a quantum teleportation system, comprising: teleporting the first quantum bit, the teleporting comprising: performing a Bell state measurement of a quantum system comprising interfering one or more first photons carrying a first quantum bit and one or more second photons carrying a second quantum bit, the quantum system including one of the first photons and one of the second photons; detecting one or more third photons, each of the third photons being confounded with one of the second photons prior to the interfering step; reading out the state of the first qubit using a Bell state measurement; obtaining arrival times of the first and second photons at detectors D1, D2 used to perform a Bell state measurement and the arrival time of the third photon at a receiver, the arrival times being tagged with reference to a clock signal such that one or more sets of photons may be identified, each set including one of the first photons, one of the second photons and one of the third photons; reading the state of the first quantum bit; and benchmarking the quantum teleportation system in real time using the arrival times; A method comprising:

[0096] [Example 14] A method according to Example 13, comprising using the quantum teleportation system of any of Examples 1 to 12.

[0097] [Example 15] A physical layer 1080 useful for implementing an Internet network, the physical layer including any of the teleportation systems of Examples 1-14, and including hardware including one or more circuits (e.g., integrated circuits, e.g., PHY chips) and / or photonic integrated circuits and / or optical devices coupled or connected thereto.

[0098] [Example 16] In the physical layer described in Example 15, the physical layer defines how to transmit streams of raw bits over the physical data links connecting the network nodes, and specifies at least one of the shapes and characteristics of electrical and optical connectors (e.g., optical fibers), the frequencies to broadcast, the line codes to use, and similar low-level parameters or others that underlie higher-level functions in the network. In one or more examples, the physical layer performs symbol encoding, transmission, reception, and decoding (e.g., bit-by-bit or symbol-by-symbol delivery of data over the physical transmission medium) and provides an interface to the transmission medium, including mechanical specifications for connectors and cables.

[0099] [Example 17] In any of the systems (100) and / or physical layers of embodiments 1 to 16 that operate under or by a control plane layer, the control plane layer is directed / coordinated by the application layer above, and the necessary requirements of the application are input to the control plane layer so that the control plane layer appropriately reconfigures the teleportation system or one or more of the devices (e.g., transmitter, receiver, clock distribution system, data collection system) within the teleportation system (100) and / or physical layer based on the needs of the client interacting with the application layer.

[0100] [Example 18] In a system (100) described in any of Examples 1 to 16, the application layer and / or the control plane layer receives a benchmark, and / or the control plane layer is instructed by the application layer using or taking into account the benchmark, and / or the control plane layer reconfigures the teleportation system using the benchmark.

[0101] [Example 19] A quantum internet or quantum network comprising a system according to any one of Examples 1 to 18.

[0102] [Example 20] A network comprising the network of Example 19 or the Internet, wherein the network is extended or interconnected to other computers using a benchmark and one or more quantum transducers.

[0103] [Example 21] In any of the systems or networks described in Examples 1-10, the benchmarking includes a network benchmark using the arrival times and the model to output a measurement or determination or test of one or more figures of merit or performance indicators of a network or system for communicating or transmitting data, the figures of merit including at least one of a transmission speed, a data transfer rate (upload speed or download speed), a latency, a throughput or reliability, a packet loss for data transmitted by or through the system or network using the first quantum bit and entangled photons.

[0104] [Example 22] A system as described in any of Examples 1 to 21, wherein the benchmark compares the numerical value of a benefit or index as a function of the client's usage at different times of day with a benefit or performance metric index provided by a user or client or another network, standard or specification.

[0105] [Example 23] In a system described in any of the above embodiments, the benchmark uses arrival time to output / determine a figure of merit or performance index and validates that arrival time is associated with successful data transfer using the model.

[0106] [Example 24] 11. The system of any of the preceding embodiments, comprising a loop quantum system.

[0107] [Example 25] A system according to any of the preceding embodiments, further comprising:

[0108] [Example 26] In a system described in any of Examples 1 to 25, the benchmark uses classical time tagging of the quantum channel and benchmarking and validation of the quantum channel to perform real-time analysis of data including data transmission rate and fidelity transmitted via teleportation, the system.

[0109] [Example 27] In a system described in any of Examples 1 to 26, the clock distribution system 122 and / or the quantum teleportation system 100 are coupled to or include a synchronization system described in [Reference 84], for example, so that the clocks of different nodes are synchronized, and signal photons are tagged using clock photons.

[0110] (Hardware environment) 10 is an exemplary hardware and software environment 1000 (referred to as a computer-implemented system and / or a computer-implemented method) that may be used to implement one or more embodiments of the present invention and that may be used to perform benchmarks, for example, and that is connected to a teleportation system 100. In one or more examples, the computer system may include or be coupled to a physical layer 1080. The hardware and software environment includes a computer 1002 and may include peripheral devices. The computer 1002 may be a user / client computer, a server computer, or a database computer. The computer 1002 includes a hardware processor 1004A and / or a special purpose hardware processor 1004B (hereinafter alternatively collectively referred to as processor 1004) and a memory 1006, such as a random access memory (RAM). The computer 1002 may be coupled to and / or integrated with other devices including input / output (I / O) devices such as a keyboard 1014, a cursor control device 1016 (e.g., a mouse, pointing device, pen and tablet, touch screen, multi-touch device, etc.), and a printer 1028. In one or more embodiments, the computer 1002 may be coupled to or include a portable or media viewing / listening device 1032 (e.g., an IPAD®, portable digital video player, cellular device, personal digital assistant, etc.). In yet other embodiments, the computer 1002 may include a multi-touch device, a mobile phone, a gaming system, or an Internet-enabled device that runs on a variety of platforms and operating systems.

[0111] In one embodiment, computer 1002 operates by hardware processor 1004A executing instructions defined by computer programs 1010 (e.g., control or benchmark applications) under the control of operating system 1008. Computer programs 1010 and / or operating system 1008 may be stored in memory 1006 and may interface with users and / or other devices to accept inputs and commands and provide outputs and results based on such inputs and commands and instructions defined by computer programs 1010 and operating system 1008.

[0112] The output / results may be presented on a display 1022 or provided to another device for presentation or further processing or action. In one embodiment, the display 1022 includes a liquid crystal display (LCD) having multiple separately addressable liquid crystals. Alternatively, the display 1022 may include a light emitting diode (LED) display having a cluster of red, green and blue diodes driven together to form a full color pixel. Each liquid crystal or pixel of the display 1022 changes to an opaque or translucent state in response to data or information generated by the processor 1004 from application of instructions of the computer program 1010 and / or the operating system 1008 to input and commands, and forms part of an image on the display. The image may be provided through a graphical user interface (GUI) module 1018. Although the GUI module 1018 is depicted as a separate module, instructions to perform GUI functions may be resident or distributed in the operating system 1008, the computer program 1010, or may be implemented in special purpose memory and processors.

[0113] In one or more embodiments, the display 1022 is integrated with / embedded in the computer 1002 and includes a multi-touch device having a touch-sensing surface (e.g., a trackpod or touch screen) capable of recognizing the presence of two or more contact points with the surface. Examples of multi-touch devices include mobile devices (e.g., IPHONE, NEXUS S, DROID devices, etc.), tablet computers (e.g., IPAD, HP TOUCHPAD, SURFACE devices, etc.), portable / handheld game / music / video player / console devices (e.g., IPOD TOUCH®, MP3 players, etc.), touch tables and walls (e.g., images projected through acrylic and / or glass and images backlit with LEDs).

[0114] Some or all of the operations performed by the computer 1002 according to the instructions of the computer program 1010 may be implemented in the special purpose processor 1004B. In this embodiment, some or all of the instructions of the computer program 1010 may be implemented via firmware instructions stored in the special purpose processor 1004B or in a read only memory (ROM), programmable read only memory (PROM) or flash memory in the memory 1006. The special purpose processor 1004B may also be hardwired through circuit design to perform some or all of the operations for implementing the present invention. Furthermore, the special purpose processor 1004B may be a hybrid processor including dedicated circuits for performing a subset of functions and other circuits for performing general functions by responding to the instructions of the computer program 1010. In one embodiment, the special purpose processor 1004B is an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA).

[0115] The computer 1002 may also implement a compiler 1012 that allows applications or computer programs 1010 written in a programming language such as C, C++, Assembly, SQL, PYTHON, PROLOG, MATLAB, RUBY, RAILS, HASKELL, or other languages, to be converted into code readable by the processor 1004. Alternatively, the compiler 1012 may be an interpreter that executes instructions / source code directly, converts source code into an intermediate representation for execution, or executes stored compiled code. Such source code may be written in a variety of programming languages ​​such as JAVA, JAVASCRIPT, PERL, BASIC, etc. Once complete, the application or computer program 1010 uses relationships and logic generated using the compiler 1012 to access and manipulate data received from I / O devices and stored in the memory 1006 of the computer 1002.

[0116] Computer 1002 also optionally includes external communications devices such as a modem, a satellite link, an Ethernet card, or other device for accepting input from and providing output to other computers 1002 .

[0117] In one embodiment, the instructions implementing the operating system 1008, the computer program 1010 and the compiler 1012 are tangibly embodied in a non-transitory computer readable medium, e.g., a data storage device 1020, which may include one or more fixed or removable data storage devices, such as a zip drive, a floppy disk drive 1024, a hard drive, a CD-ROM drive, a tape drive, etc. Additionally, the operating system 1008 and the computer program 1010 include computer program 1010 instructions that, when accessed, read and executed by the computer 1002, cause the computer 1002 to perform the steps necessary to implement and / or use the present invention or to load a program of instructions into the memory 1006, thus creating special purpose data structures that cause the computer 1002 to operate as a specially programmed computer that performs the method steps described herein. The computer program 1010 and / or operating instructions may also be tangibly embodied in the memory 1006 and / or the data communication device 1030, thereby creating a computer program product or article of manufacture in accordance with the present invention. Thus, as used herein, the terms "article of manufacture," "program storage device," and "computer program product" are intended to encompass a computer program accessible from any computer-readable device or media.

[0118] Of course, those skilled in the art will recognize that any combination of the above components or any number of different components, peripherals and other devices may be used in conjunction with computer 902 .

[0119] 11 illustrates a schematic diagram of a typical distributed / cloud-based computer system 1100 that uses a network 1104 to connect a client computer 1102 to a server computer 1106. A typical combination of resources may include the network 1104, including the Internet, LANs (local area networks), WANs (wide area networks), SNA (systems network architecture) networks, etc., the client 1102 (as defined in FIG. 10) being a personal computer or workstation, and the server 1106 (as defined in FIG. 10) being a personal computer, workstation, minicomputer, or mainframe. However, it should be noted that different networks, such as a cellular network (e.g., global system for mobile communications (GSM) or otherwise), a satellite-based network, or any other type of network, may be used to connect the client 1102 and the server 1106 in accordance with an embodiment of the present invention.

[0120] A network 1104, such as the Internet, connects the clients 1102 to the server computers 1106. The network 1104 may utilize Ethernet, coaxial cable, wireless communication, radio frequency (RF), etc. to connect and provide communication between the clients 1102 and the server computers 1106. Furthermore, in a cloud-based computing system, the resources (e.g., storage, processors, applications, memory, infrastructure, etc.) of the clients 1102 and the server computers 1106 may be shared by the clients 1102, the server computers 1106, and users across one or more networks. Resources may be shared by multiple users and dynamically reallocated per demand. In this regard, cloud computing may be referred to as a model for enabling access to a shared pool of configurable computing resources.

[0121] The client 1102 may execute a client application or web browser and communicate with a server computer 1106 executing a web server 1110. Such a web browser is typically a program such as MICROSOFT INTERNET EXPLORER / EDGE, MOZILLA FIREFOX, OPERA, APPLE SAFARI, GOOGLE CHROME, etc. Additionally, software executed on the client 1102 may be downloaded from the server computer 1106 to the client computer 1102 and installed as a web browser plug-in or an ACTIVEX control. Thus, the client 1102 may utilize ACTIVEX component / component object model (COM) or distributed COM (DCOM) components to provide a user interface on the display of the client 1102. The web server 1110 is typically a program such as MICROSOFT'S INTERNET INFORMATION SERVER.

[0122] The web server 1110 can host Active Server Page (ASP) or Internet Server Application Programming Interface (ISAPI) applications 1112 that execute scripts. The scripts call objects (called business objects) that execute business logic. The business objects manipulate data in a database 1116 through a database management system (DBMS) 1114. Alternatively, the database 1116 may be part of the client 1102 or connected directly to the client 1102, instead of communicating / retrieving information from the database 1116 across the network 1104. When developers encapsulate business functionality in objects, the system may be referred to as a Component Object Model (COM) system. Thus, scripts running on the web server 1110 (and / or applications 1112) call COM objects that implement the business logic. Furthermore, the server 1106 can utilize MICROSOFT'S TRANSACTION SERVER (MTS) to access the required data stored in the database 1116 through interfaces such as Active Data Objects (ADO), Object Linking and Embedding DataBase (OLE DB) or Open DataBase Connectivity (ODBC).

[0123] In general, all of these components 1100-1116 include logic and / or data embodied in and / or retrievable from a device, medium, signal or carrier, such as a data storage device, a data communication device, a remote computer or device coupled to a computer via a network or via another data communication device, which logic and / or data, when read, executed and / or interpreted, results in the steps necessary to implement and / or use the present invention being performed.

[0124] Reference is made herein to the terms "user computer," "client computer," and / or "server computer," with the understanding that such computers 1102 and 1006 may be interchangeable and may further include thin-client devices having limited or full processing capabilities, portable devices such as mobile phones, notebook computers, pocket computers, multi-touch devices, and / or any other devices having suitable processing, communication, and input / output capabilities.

[0125] Of course, one skilled in the art will recognize that any combination of the above components or any number of different components, peripherals and other devices may be used with the computers 1002 and 1006. An embodiment of the present invention is implemented as a software application on the client 1002 or server computer 1006. Furthermore, as mentioned above, the client 1002 or server computer 1006 may include a thin client device or a portable device with a multi-touch based display. The entire teleportation system 100 may be operated under a control plane layer (like the physical layer of the current Internet) that is directed / coordinated by an application layer above. Based on the needs of the client interacting with the application layer, the necessary requirements of the application are input to the control plane layer, which appropriately reconfigures the various above-mentioned devices involved in the teleportation system 100. If sufficiently efficient quantum transducers (devices capable of converting photons to microwaves and back) are developed, the teleportation system 100 through interaction with these transducers may help to extend the network to a continental scale, increasing computing power by interconnecting different quantum computers.

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[0127] (Conclusion) This completes the description of the preferred embodiments of the present invention. The foregoing description of one or more embodiments of the present invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teachings. It is intended that the scope of the invention be limited not by this detailed description, but rather by the appended claims.

Claims

1. 1. A quantum teleportation system comprising: a transmitter that generates a first photon; a source of pairs of entangled photons, each pair including a second photon entangled with a third photon; a coupler electromagnetically coupled to the transmitter and to the source of entangled photon pairs; a pair of detectors D1 and D2 electromagnetically coupled to the coupler; a receiver including a detection system including a detector D3 for detecting the third photon; an optical fiber connecting the detector D3 and a source of the entangled photon pairs, the detector D3 detecting the third photon transmitted along the optical fiber; a clock distribution system that outputs one or more clock signals that control timing of the first photon, the second photon, and the third photon; the coupler causes one of the first photons carrying a first quantum bit and one of the second photons carrying a second quantum bit to interact with each other to form interference; the pair of detectors D1 and D2 detects the interference used to obtain a Bell state measurement of a quantum system including the first qubit and the second qubit; the detector D3 detects one of the third photons entangled with one of the second photons and outputs a signal in response thereto; and The detection system uses the signal and the Bell state measurement to read out the state of the first qubit. a clock distribution system that outputs the clock signal; a data collection system that collects arrival times of the first and second photons at the detectors D1 and D2 and the arrival time of the third photon at the detector D3, the arrival times being tagged with reference to the clock signal such that one or more sets of photons are identified, each set including one of the first photons, one of the second photons, and one of the third photons; and a computer that benchmarks the quantum teleportation system in real time using the arrival times, the benchmarking including using a model that simulates at least one of the fidelity of teleportation of the first qubit teleported to one of the third photons received at the detector D3, or the degree of indistinguishability between one of the first photons and one of the second photons as a function of the average number of the second photons, the model being calibrated and validated using experimental measurements of the fidelity of teleportation and the degree of indistinguishability; A quantum teleportation system comprising:

2. 2. The system of claim 1, the transmitter generating pulses of electromagnetic radiation each including one or more of the first photons; The system further comprises: a first attenuator that attenuates the pulses of electromagnetic radiation to output attenuated pulses each including a first average number of the first photons, the first average number of the first photons received at the combiner increasing the likelihood that the combiner will cause one of the first photons to interact with one of the second photons to form the interference; a first filter electromagnetically coupled to the coupler and configured to spectrally filter electromagnetic radiation to increase indistinguishability between one of the first photons and one of the second photons; one or more second filters electromagnetically coupled to a source of the entangled photon pairs and configured to spectrally filter the entangled photons; Equipped with the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early and a late arriving photon; and The source of the entangled photons includes a laser that excites a nonlinear material to output the second photons, which include idler photons, and the third photons, which include signal photons, according to a spontaneous parametric down-conversion (SPDC) process. It is a system.

3. 2. The system of claim 1, wherein the benchmarking includes determining at least one of: a fidelity of teleportation of the first quantum bit teleported to one of the third photons received at D3, a degree of the indistinguishability between one of the first photons and one of the second photons, or a coincident photon detection rate of three times that of one of the photons detected coincidentally at each of D1, D2 and D2.

4. 10. The system of claim 1, wherein the combiner comprises a beam splitter or a linear optical device capable of interfering photons or electromagnetic fields.

5. 2. The system of claim 1, the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early and a late arriving photon; the source of the entangled photons includes a laser that excites a nonlinear material to output one of the second photons comprising an idler photon and one of the third photons comprising a signal photon according to a spontaneous parametric down-conversion (SPDC) process; the clock signal includes clock cycles; The data collection system measures the average number of second photons by comparing: a coincidence rate including events in which one of the second photons and one of the third photons in one of the entangled photon pairs are detected in the same one of the clock cycles; and a contingency rate comprising an event in which one of the second photons and one of the third photons in one of the entangled photon pairs are detected in different clock cycles; measuring the average number of second photons by comparing The degree of indistinguishability is measured by performing a Hon-Mandel experiment in which the coupler includes a beam splitter and the interference is observed; and The fidelity of the teleportation is measured using an interferometer that measures the visibility of the interference of the third photon with itself. It is a system.

6. 6. The system of claim 5, wherein the model calculates the fidelity of the teleportation and the degree of indistinguishability, the calculation comprising: The probability P of coincident detection of one of the photons by a factor of three at each of the detectors D1, D2 and D3 is ３ｆ , i.e. [0010] where φ ｍａｘ (φ ｍｉｎ ) is the maximum (minimum) phase added to one path of the second photon, corresponding to the three times coincidence detection rate; and The system calculates by performing the following:

7. 7. The system of claim 6, [0025] where η ｉ and η ｓ are the transmission efficiencies of the second photons and the third photons, respectively, including the efficiency of the detector, μA is the average number of the first photons per time bin, and μB is the average number of second photons per time bin.

8. 8. The system of claim 7, the first qubit comprises a first time bin qubit, and the second qubit comprises a second time bin qubit; the clock signal includes clock cycles; The data collection system includes: a coincidence rate that includes events in which one of the second photons and one of the third photons in one of the entangled photon pairs are detected in the same one of the clock cycles; and a contingency rate including an event in which one of the second photons and one of the third photons in one of the entangled photon pairs are detected in different clock cycles; a first detection rate of the second photons; and a second detection rate of the third photons; and Get η ｉ is the second detection rate divided by the match rate, and η ｓ is the first detection rate divided by the match rate, and The average number of the second photons per time bin is the chance rate divided by the coincidence rate.

9. 5. The system of claim 4, wherein the model calculates the probability that the detectors D1, D2 and D3 receive one of the first photons, one of the second photons and one of the third photons in the same clock cycle using fitting parameters including a transmittance representing the indistinguishable quantities.

10. 3. The system of claim 2, wherein the computer uses the benchmark to output feedback used to optimize at least one of the timing, the intensity of the entangled photons output from a source of the entangled photons, the spectral filtering of the photons, or the attenuation of the pulse of electromagnetic radiation to achieve a teleportation fidelity of greater than 0.90 when the third photon travels a distance of at least 22 kilometers along the optical fiber.

11. 10. The system of claim 1, further comprising a display for displaying the benchmark.

12. 1. A method of teleporting using a quantum teleportation system, comprising: teleporting a first quantum bit, the teleporting comprising: performing a Bell state measurement of a quantum system comprising interfering one or more first photons carrying the first quantum bit and one or more second photons carrying the second quantum bit, the quantum system including one of the first photons and one of the second photons; detecting one or more third photons, each of the third photons being confounded with one of the second photons prior to the interfering step; reading out the state of the first qubit using the Bell state measurement; obtaining arrival times of the first and second photons at detectors D1, D2 used to perform the Bell state measurement and the arrival time of the third photon at the receiver, the arrival times being tagged with reference to a clock signal such that one or more sets of photons may be identified, each set including one of the first photons, one of the second photons and one of the third photons; reading the state of the first quantum bit; and benchmarking the quantum teleportation system in real time using the arrival times; A method comprising:

13. 1. A computer implemented system comprising one or more processors, one or more memories, and an application stored in the one or more memories, The application is executed by one or more processors to benchmark a quantum teleportation system in real time, the quantum teleportation system comprising: teleporting a first quantum bit, performing a Bell state measurement of a quantum system, the measurement comprising the sub-steps of interfering one or more first photons carrying the first quantum bit and one or more second photons carrying a second quantum bit, the quantum system including one of the first photons and one of the second photons; detecting one or more third photons at a receiver, each of the third photons being entangled with one of the second photons prior to the interference; teleporting the first quantum bit; reading out the state of the first qubit using the Bell state measurement; The purpose of the present invention is to The benchmarking includes the application, the application comprising: receiving arrival times of the first and second photons at detectors D1, D2 used to perform the Bell state measurement, and the arrival time of the third photon at the receiver, the arrival times tagged with reference to a clock signal such that one or more sets of photons can be identified, each set including one of the first photons, one of the second photons and one of the third photons; and using the arrival times to determine at least one of: a fidelity of teleportation of the first quantum bit teleported to one of the third photons received at D3, a degree of indistinguishability of one of the first photons and one of the second photons, or a three-fold coincident photon detection rate at which one of the photons is detected coincidentally at each of D1, D2, and D2; 4. A computer-implemented system for

14. 14. The system of claim 13, further comprising: a transmitter generating pulses of electromagnetic radiation each including one or more of said first photons; a first attenuator that attenuates the pulses of electromagnetic radiation to output attenuated pulses each including a first average number of the first photons, the first average number of photons received on a combiner such that the combiner increases the likelihood that one of the first photons will interact with one of the second photons to form interference; a first filter electromagnetically coupled to the coupler and configured to spectrally filter electromagnetic radiation to increase indistinguishability between one of the first photons and one of the second photons; one or more second filters electromagnetically coupled to a source of entangled photon pairs (including one of the second photons and one of the third photons) and configured to spectrally filter the entangled photons; Equipped with the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early and a late arriving photon; and The system, wherein the source of the pair of entangled photons includes a laser that excites a nonlinear material to output the second photon comprising an idler photon and the third photon comprising a signal photon according to a spontaneous parametric down-conversion (SPDC) process.

15. In the system described in Example 13, the benchmarking includes using a model to simulate at least one of the teleportation fidelity of the first quantum bit teleported to one of the third photons received at the detector D3 or the degree of indistinguishability between one of the first photons and one of the second photons as a function of the average number of the second photons, and the model is calibrated and validated using experimental measurements of the teleportation fidelity and the degree of indistinguishability.

16. 15. The method of claim 14, wherein the combiner comprises a beam splitter or a linear optical device capable of interfering photons or electromagnetic fields.

17. 15. The method of claim 14, the first qubit and the second qubit each include a time bin qubit that includes a superposition of an early and a late arriving photon; the source of the entangled photons includes a laser that excites a nonlinear material to output one of the second photons comprising an idler photon and one of the third photons comprising a signal photon according to a spontaneous parametric down-conversion (SPDC) process; the clock signal includes clock cycles; The data collection system includes: a coincidence rate involving an event in which one of the second photons and one of the third photons in the entangled photon pair are detected in the same one of the clock cycles; and a contingency rate comprising an event in which one of the second photons and one of the third photons in the entangled pair are detected in different clock cycles; measuring the average number of second photons by comparing the degree of indistinguishability is measured by performing a Hon-Mandel experiment using the coupler including a beam splitter to observe the interference; and A method, wherein the fidelity of the teleportation is measured using an interferometer that measures the visibility of the interference of the third photon with itself.

18. 16. The system of claim 15, The model calculates the fidelity of the teleportation and the amount of indistinguishability, this calculation comprising: The probability P of coincident detection of one of the photons by a factor of three at each of the detectors D1, D2 and D3 is ３ｆ , i.e. [0030] ζ is the amount of indistinguishability between the first quantum bit and the second quantum bit, and ζ=1 (ζ=0) corresponds to the case where both the first quantum bit and the second quantum bit are completely indistinguishable (distinguishable). determining the indistinguishable amount; and The fidelity of said teleportation, i.e. [0045] where φ ｍａｘ (φ ｍｉｎ ) is the maximum (minimum) phase added to one path of the second photon and corresponds to the maximum (minimum) of the three times coincidence detection rate; The system calculates by performing the following:

19. 20. The system of claim 18, [0050] where η ｉ and η ｓ are the transmission efficiencies of the second photons and the third photons, respectively, including the efficiency of the detector, μA is the average number of the first photons per time bin, and μB is the average number of second photons per time bin.

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