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arXiv:2107.01304 · Entropy

Qubit-Based Clock Synchronization for QKD Systems Using a Bayesian Approach

Roderick Cochran, Daniel J. Gauthier

Published Jul 30, 2021• 27 citations
arXivHTMLPDF

Abstract

Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users' clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware. Previous qubit-based synchronization protocols sacrifice secure key either directly or indirectly, and all known qubit-based synchronization protocols do not efficiently use all publicly available information published by the users. Here, we introduce a Bayesian probabilistic algorithm that incorporates all published information to efficiently find the clock offset without sacrificing any secure key. Additionally, the output of the algorithm is a probability, which allows us to quantify our confidence in the synchronization. For demonstration purposes, we present a model system with accompanying simulations of an efficient three-state BB84 prepare-and-measure protocol with decoy states. We use our algorithm to exploit the correlations between Alice's published basis and mean photon number choices and Bob's measurement outcomes to probabilistically determine the most likely clock offset. We find that we can achieve a 95 percent synchronization confidence in only 4140 communication bin widths, meaning we can tolerate clock drift approaching 1 part in 4140 in this example when simulating this system with a dark count probability per communication bin width of 8×10-4 and a received mean photon number of 0.01.

DOI
10.3390/e23080988

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Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users' clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware. Previous qubit-based synchronization protocols sacrifice secure key either directly or indirectly, and all known qubit-based synchronization protocols do not efficiently use all publicly available information published by the users. Here, we introduce a Bayesian probabilistic algorithm that incorporates all published information to efficiently find the clock offset without sacrificing any secure key. Additionally, the output of the algorithm is a probability, which allows us to quantify our confidence in the synchronization. For demonstration purposes, we present a model system with accompanying simulations of an efficient three-state BB84 prepare-and-measure protocol with decoy states. We use our algorithm to exploit the correlations between Alice's published basis and mean photon number choices and Bob's measurement outcomes to probabilistically determine the most likely clock offset. We find that we can achieve a 95 percent synchronization confidence in only 4140 communication bin widths, meaning we can tolerate clock drift approaching 1 part in 4140 in this example when simulating this system with a dark count probability per communication bin width of 8×10-4 and a received mean photon number of 0.01.
Quantum key distribution (QKD) enables the generation of information-theoretic secure keys between two remote parties. A critical component of successful QKD implementation is the effective synchronization of clocks between these users. Traditional methods of locking to a reference clock or transmitting a synchronization signal rely on auxiliary equipment, which increases the complexity and cost, thus hindering the widespread deployment of QKD. Here, we propose a method to achieve clock and pulse synchronization by exploiting a subset of the transmitted qubits. We demonstrate our scheme with a time-bin phase-coding BB84 QKD system and verify the realization of long-term stable key generation over distances of 50 km and 100 km. Our method simplifies the implementation of QKD systems and introduces new possibilities for synchronization algorithms in other quantum communication protocols.
Time synchronization is a crucial requirement in quantum key distribution (QKD)8 protocols, ensuring accurate key generation via the correct assignment of bits of raw key and9 enabling eavesdropping detection via the precise recording of photon statistics. State-of-the-art10 experiments typically use an extra channel to synchronize the clocks of the transmitter and receiver11 via classical signals. In this work, we study the possibility of performing clock synchronization12 via the signals used for the key generation, which are already present in decoy-state-based BB8413 protocols.14 Without altering the protocol in any way, we use the different mean photon numbers of the15 signal and decoy states for time synchronization without a dedicated physical channel capable of16 clock synchronization. The proposed method relies only on the photons sent and received for17 key generation and does not require any change to the QKD protocol. The only change in the18 experiment is on the software level, thus making it very simple to implement.19 We demonstrate clock synchronization method in a simulation of a specific fiber-based QKD20 experiment. Like other decoy-state-based BB84 protocols, it is based on weak coherent pulses.21 In this simulation, we investigate the parameter space to find limits and optimal choices of our22 proposed method.23 In addition to the non-protocol-altering clock synchronization method, we also discuss an24 approach that significantly improves performance in lossy channels by introducing an additional25 decoy state with a very high mean photon number.26 By eliminating the need for an extra channel capable of clock synchronization, both methods27 proposed potentially reduce the complexity and cost of QKD systems and improve their agility
Quantum key distribution allows for a provably secure transmission of cryptographic keys over an optical channel. Encoded polarization states or time-bin degree of freedom have been used for successful demonstrations. However, photon losses in long fibers, slow single photon detectors, and detector dark counts significantly limit the overall bit rate. Improving key throughput and reducing the overhead of key reconciliation remain as major challenges. Methods which utilize multiple time bins allow for multiple key bits to be encoded in a single photon, thus increasing the fidelity of transmitted keys and decreasing the overhead of key reconciliation in real-world conditions. Previous implementations of these methods required that Alice and Bob share a time reference by sharing a dedicated classical channel used for synchronization. This work presents a technique that allows two parties to exchange time-bin encoded photons without the need for synchronized time references. Our technique uses a framing protocol which allows Alice to encode a time reference along with a key which is determined by Alice before transmission. Security can be achieved by monitoring the visibility of a pair of Franson interferometers, using decoy pulses and measuring the round trip time between Alice and Bob. The bit rate of this technique is limited only by the recovery time of the detector and the speed of the modulation electronics. We experimentally demonstrate a raw bit rate of 5Mb/s over an optical channel with 55dB of loss, which is competitive with current research. We also demonstrate absolute timing synchronization with an accuracy of 20ps.
We propose Qubit4Sync, a synchronization method for quantum-key-distribution (QKD) setups, based on the same qubits exchanged during the protocol and without requiring additional hardware other than that necessary to prepare and measure the quantum states, in a similar fashion to the clock recovery used in classical communications. Our approach introduces a cross-correlation algorithm with low computational complexity for high channel losses. We test the robustness of our scheme in a real QKD implementation, and we believe it may find application in other quantum communication protocols.
Clock synchronization is critical for maintaining low error rates in quantum key distribution. Here, we describe how a frequency mismatch between the transmitter and receiver clocks affects the quantum bit error rate in quantum key distribution, and derive from this model a simple synchronization algorithm together with clock stability requirements for practical operation. Our algorithm continuously compensates for both frequency mismatch and time-offset fluctuations directly from detection timestamps. It does not require a dedicated synchronization channel or auxiliary qubit sequence, converges from a large frequency mismatch within approximately one second of photon acquisition, and remains effective in low-photon-count regimes (more than 30 dB of channel loss) using standard hardware. We validate our approach by demonstrating successful key exchange over 100 km of fiber and continuous operation over 24 hours in a 16 km metropolitan network using commercial systems, with performance equivalent to using a service channel for clock synchronization.
Time synchronization is crucial for quantum key distribution (QKD) systems. In order to compensate for the time drift caused by the Doppler effect and adapt to the unstable optical link in satellite-to-ground QKD, previous demonstrations generally adopted synchronization methods requiring additional hardware. In this paper, we present a novel synchronization method based on the detected quantum photons, thus simplifying additional hardware and reducing the complexity and cost. This method adopts target frequency scanning to realize fast frequency recovery, utilizes polynomial fitting to compensate for the Doppler effect, and takes use of the vacuum state in the decoy-state BB84 protocol to recover the time offset. This method can avoid the influence of synchronization light jitter, thus improving the synchronization precision and the secure keys as well. Successful satellite-to-ground QKD based on this new synchronization scheme has been conducted to demonstrate its feasibility and performance. The presented scheme provides an effective synchronization solution for quantum communication applications.