PaperlayerView exact revision on arXiv

Source-linked AI summary

Breaking the Rate-Loss Bound of Quantum Key Distribution with Asynchronous Two-Photon Interference

Yuan-Mei Xie, Yu-Shuo Lu, Chen-Xun Weng, Xiao-Yu Cao, Zhao-Ying Jia, Yu Bao, Yang Wang, Yao Fu, Hua-Lei Yin, Zeng-Bing Chen

arXiv:2112.11635v3quant-phcs.CRphysics.optics

TL;DR

Repeaterless QKD is bounded by the PLOB capacity, while twin-field protocols require phase-tracking and phase-locking infrastructure. The paper introduces asynchronous-MDIQKD, which postmatches phase-correlated interference events through time multiplexing. It reaches 450 km without phase tracking and beats the PLOB bound at 270 km after also removing phase locking.

  • Problem

    Twin-field protocols require phase tracking and phase locking to compensate channel and laser phase fluctuations, increasing complexity and hindering free-space implementation.

  • Method

    The protocol uses time multiplexing to postmatch two phase-correlated single-photon interference detection events into an asynchronous two-photon Bell state.

  • Results

    A 1 GHz system reaches 450 km without phase tracking and beats the PLOB bound at 270 km after phase locking is also removed.

  • Takeaways & Limitations

    The protocol offers a simpler MDIQKD implementation with higher key rates than PMQKD and longer transmission than AOPP under imperfect intensity modulation.

Abstract

from arXiv · show

Twin-field quantum key distribution can overcome the secret key capacity of repeaterless quantum key distribution via single-photon interference. However, to compensate for the channel fluctuations and lock the laser fluctuations, the techniques of phase tracking and phase locking are indispensable in experiment, which drastically increase experimental complexity and hinder free-space realization. Inspired by the duality in entanglement, we herein present an asynchronous measurement-device-independent quantum key distribution protocol that can surpass the secret key capacity even without phase tracking and phase locking. Leveraging the concept of time multiplexing, asynchronous two-photon Bell-state measurement is realized by postmatching two interference detection events. For a 1 GHz system, the new protocol reaches a transmission distance of 450 km without phase tracking. After further removing phase locking, our protocol is still capable of breaking the capacity at 270 km. Intriguingly, when using the same experimental techniques, our protocol has a higher key rate than the phase-matching-type twin-field protocol. In the presence of imperfect intensity modulation, it also has a significant advantage in terms of the transmission distance over the sending-or-not-sending type twin-field protocol. With high key rates and accessible technology, our work provides a promising candidate for practical scalable quantum communication networks.

I. INTRODUCTION

Conventional QKD is constrained by the PLOB bound, while twin-field protocols overcome this scaling but require complex phase-tracking and phase-locking systems. The proposed asynchronous-MDIQKD protocol uses time multiplexing to remove these requirements while retaining favorable key-rate scaling.

  • The PLOB bound R = −log2(1 − η) rigorously limits the key rate of most repeaterless QKD protocols, including MDIQKD.
  • Twin-field QKD and variants such as SNSQKD and PMQKD increase the key-rate scaling to O(√η), overcoming the PLOB bound.
  • Phase tracking compensates channel phase fluctuations but introduces scattering noise, occupies quantum-signal time, and imposes high detector-counting requirements.
  • Phase locking requires additional reference-light channels, while some implementations introduce security risks or complicated feedback systems.
  • The proposed asynchronous-MDIQKD protocol postmatches two phase-correlated detection events using time multiplexing, enhancing key-rate scaling from O(η) to O(√η).
  • Without phase tracking and phase locking, the protocol can beat the PLOB bound at approximately 270 km and supports longer distance and higher key rates than comparison protocols under imperfect modulation.

II. ASYNCHRONOUS-MDIQKD PROTOCOL

This section introduces the asynchronous-MDIQKD protocol before giving its detailed description.

  • The protocol is introduced through its basic idea before the paper presents a detailed protocol description.
  • The section separates the conceptual introduction of asynchronous-MDIQKD from the subsequent operational details.
  • The paper proceeds from an initial protocol overview to a detailed description.

A. Protocol topology

The protocol replaces spatial multiplexing and neighboring-bin coincidence requirements with time multiplexing: independent single-photon interference events are postmatched into asynchronous Bell states within a short interval.

  • Protocol topology: The adaptive MDIQKD motivation uses m spatial channels so arriving single photons can be paired at Charlie.
  • Protocol topology: Time-bin MDIQKD encodes information in the relative phase between two separate time bins i and j.
  • Protocol topology: The asynchronous protocol performs single-photon interference across N time bins and postmatches two phase-correlated successful detections to establish Bell states.The resulting key-rate decay is O(√η).
  • Protocol topology: Detection events are paired within Tc, distinguishing events with nearby partners from isolated case 2 events.The differential phase evolution of events within Tc is treated as nearly identical but unknown.
  • Protocol topology: Alice and Bob prepare phase-randomized weak coherent pulses, while Charlie interferes them with a beam splitter and announces single-detector clicks.
  • Protocol topology: A sufficiently small number of isolated case 2 events—one on average—does not affect protocol security.

B. Protocol description

The protocol prepares decoy-state weak coherent pulses, publicly announces single-detector interference events, postmatches compatible events, estimates security parameters, and performs classical key distillation.

  • B. Protocol description: Alice and Bob repeat pulse preparation for N rounds, randomly choosing basis bits and phase-randomized signal, decoy, and vacuum intensities.
  • B. Protocol description: Charlie records an event when exactly one detector clicks and publicly announces both the event and the clicking detector.
  • B. Protocol description: In sifting, case 2 data are discarded when their count is at most Λ; otherwise, the protocol aborts.
  • B. Protocol description: Case 1 events are randomly matched within Tc after Alice and Bob reveal relevant intensities and phase information.
  • B. Protocol description: Z-basis matched events generate raw bits from time-bin ordering, with Bob flipping his bit to establish correlation.
  • B. Protocol description: X-basis events are matched when their phase relation is 0 or π, and decoy-state estimation determines single-photon counts, error rates, and phase errors.
  • B. Protocol description: The security analysis assumes identical independent single-photon distributions across detection events before error correction and privacy amplification produce the final key.

III. EXPERIMENTAL DISCUSSION

The protocol encodes information in the phase difference between matched time bins and uses their phase correlation to enable asynchronous postmatching. Differential phase evolution depends on laser-frequency differences and fiber-channel fluctuations, while short intervals preserve the needed correlation.

  • Protocol encoding: Information is encoded in the phase difference between two matched time bins, with one serving as reference and the other as signal.This matches the relative-phase structure of time-bin encoding MDIQKD.
  • Protocol encoding: Alice and Bob postmatch pulses from time bins i and j when their phase relation supports asynchronous two-photon entanglement generation.The postmatching condition relies on phase-correlated detection events.
  • Phase evolution: Differential phase evolution is determined by the users’ laser-frequency difference and fluctuations in the fiber channels.The received-pulse phase evolution is described separately for the two user-to-Charlie links.
  • Sifting: The sifting step lets Bob apply a detector-dependent bit flip using the announced detector pair and the global phase difference between matched time bins.RL, LR, RR, and LL denote the detector-click patterns used in this postprocessing.
  • Phase evolution: In symmetric channels, the differential phase evolution is parameterized by frequency and fiber-length differences between Alice’s and Bob’s links.The parameters include δv_i, δl_i, the average link length l_i, and average laser frequency v_i.

A. Removing phase tracking

Short-term matching preserves phase correlation sufficiently to remove phase tracking under suitable experimental conditions. The protocol therefore remains implementable with tens-of-microseconds matching intervals and adequate detection counts.

  • Phase-drift condition: 50 µs matching intervals produce approximately 0.4 rad of phase drift at 402 km, yielding an intrinsic interference error rate of approximately 1%.The estimate uses a measured relative phase drift of approximately 8 rad/ms and uniformly distributed matched time bins.
  • Implementation condition: Tens-of-microseconds matching intervals allow experimental implementation without phase tracking when sufficient detection counts are accumulated per interval.The protocol relies on naturally approximately constant differential phase evolution over short intervals.
  • Implementation condition: At 400 km, a 1 GHz system with 70% detection efficiency and ultra-low-loss fiber yields approximately 9.3 detection events per matching interval for total mean photon number 0.5.This count is described as sufficient for postmatching.
  • Frequency calibration: Figure 4 relates HOM visibility and interference error rate to the frequency difference between the two lasers for a 1 µs consecutive-time-bin interval.The blue curve represents visibility and the orange dotted curve represents error rate.

B. Removing phase tracking and phase locking

Without phase tracking and phase locking, asynchronous-MDIQKD uses short-time phase correlations and frequency calibration to control interference errors while preserving long-distance key distribution. Simulations and laser measurements support operation beyond the PLOB bound under practical conditions.

  • Phase-drift control: Short matching intervals make fiber-length drift negligible, leaving laser frequency difference as the main source of relative phase drift.For intervals of a few tens of microseconds, the phase drift is primarily determined by the frequency difference between independent lasers.
  • Phase-drift control: 100 kHz frequency difference over Tc = 1 µs produces an approximately 0.1π phase misalignment and a 2.4% interference error rate.This operating point is used to estimate the practical error budget without phase tracking or phase locking.
  • Frequency calibration: Laser beat-note measurements after manual temperature adjustment yielded mean frequency differences of 145 kHz for two NKT lasers and 92.5 kHz for two RIO Orion lasers.Automatic feedback systems could reduce the frequency difference further.
  • Frequency calibration: The HOM-based calibration method uses interference error rate to tune the two laser frequencies, reaching a minimum error rate of approximately 25% at δv = 0 and 29.7% at 100 kHz.Increasing the consecutive-bin interval τ makes the error rate more sensitive to frequency difference.
  • Simulation results: Without phase tracking, asynchronous-MDIQKD with Tc = 50 µs and F = 1 GHz breaks the PLOB bound at approximately 280 km and reaches 450 km transmission distance.The simulation uses an X-basis misalignment angle σ = π/10.
  • Simulation results: At 300 km and F = 4 GHz without phase tracking or phase locking, the X-basis error rate increases with matching interval, while δv = 10 kHz gives slow growth.The result indicates that a relatively low repetition rate can be sufficient when the frequency difference is small.

IV. PERFORMANCE AND DISCUSSION

The protocol remains effective under finite-size conditions, without phase tracking or phase locking, and in symmetric and asymmetric channels. Simulations report PLOB-bound violations, long transmission distances, and higher rates than comparison protocols.

  • Short-time matching: 270 km is achieved beyond the PLOB bound without phase tracking or phase locking.For δv = 100 kHz, 10 GHz repetition and Tc = 1 µs extend secure transmission beyond 380 km.
  • Finite-size analysis: The protocol's finite-size robustness corresponds to an approximately 1 × 10^-8 probability of exceeding the event threshold, or failure once in 100 million experimental rounds.The event count is modeled with a Poisson distribution and threshold Λ = 10.
  • Short-time matching: 450 km is reached with a 1 GHz system when phase tracking is removed, while the key rate beats the PLOB bound at 280 km.This scenario uses Tc = 50 µs, σ = π/10, and N = 10^12.
  • Protocol comparisons: 350 kbps is obtained at δv = 10 kHz and Tc = 10 µs, approximately one order of magnitude above TFQKD's 20 kbps under the compared detector-count conditions.The comparison uses 1 MHz per channel available for TFQKD versus the protocol's higher usable count rate.
  • Protocol comparisons: At 500 km in symmetric channels, the protocol's key rate is 150% higher than PMQKD and its transmission distance is 240 km longer than AOPP for N = 10^13.For N = 10^11, transmission exceeds 500 km.
  • Protocol comparisons: At 500 km in asymmetric channels, the protocol's key rate is 400% higher than PMQKD and its transmission distance is 150 km longer than AOPP for N = 10^13.The asymmetric case uses lb = la + 100 km; for N = 10^11, transmission is 50 km higher.

V. CONCLUSION

The protocol uses time multiplexing to realize asynchronous two-photon interference, achieving O(√η) key-rate scaling beyond the PLOB bound while simplifying hardware requirements. It also outperforms PMQKD and SNSQKD (AOPP) under the stated comparison conditions.

  • V. CONCLUSION: O(√η) key-rate scaling is realized through asynchronous two-photon interference, surpassing the PLOB bound.The protocol is presented as a way to overcome the linear bound of dual-rail protocols.
  • V. CONCLUSION: Removing phase locking and phase tracking greatly simplifies hardware requirements with a small sacrifice in performance.
  • V. CONCLUSION: Under the same experimental techniques as TFQKD, the protocol shows longer transmission and higher key rate than PMQKD and SNSQKD (AOPP) with imperfect intensity modulation.
  • V. CONCLUSION: Random phase modulation also allows the protocol to exploit six-state encoding.With single-photon sources in the Z basis, the protocol can be secure up to a higher error rate and achieve a higher key rate.

1. Asynchronous-MDIQKD protocol for arbitrary-time matching

The protocol postmatches detection events in arbitrary time windows and separates matched events into correct and incorrect categories for Z-basis error estimation. Its gain and error calculations account for phase slices, detector events, and statistical event-counting assumptions.

  • 1. Asynchronous-MDIQKD protocol for arbitrary-time matching: After postmatching, valid Z-basis events are divided into correct and incorrect event classes to calculate the bit error rate.The overall Z-basis event count and error rate are denoted by n_z and E_z = n_z^E/n_z.
  • 1. Asynchronous-MDIQKD protocol for arbitrary-time matching: The gain for intensity pair {k_a, k_b} is averaged over the phase difference and determines the total event count.The event count is x_kakb = N p_ka p_kb q_kakb.
  • 1. Asynchronous-MDIQKD protocol for arbitrary-time matching: Detection events are classified by neighboring-event availability within a T_c window, and case 2 events may be discarded when their count is below threshold Λ.The probabilities of the two cases depend on the total number of neighboring time bins and the average detection probability.
  • 1. Asynchronous-MDIQKD protocol for arbitrary-time matching: Phase differences are divided into M slices, with M = 16 used in simulation, and detection counts in each slice follow a Poisson distribution.Events are grouped according to phase slices δ_m.

Appendix C: Statistical fluctuation analysis

The statistical fluctuation analysis uses the Chernoff bound to estimate observed values from expected values, providing upper and lower bounds for simulation parameters.

  • Appendix C: Statistical fluctuation analysis: The simulation introduces a statistical fluctuation analysis method based on the Chernoff bound.
  • Appendix C: Statistical fluctuation analysis: For an expected value x*, the Chernoff bound supplies upper and lower bounds on the observed value.
  • Appendix C: Statistical fluctuation analysis: The resulting bounds are used to estimate real values from expected values and observed values from expected values.
Loading 2112.11635v3…