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Physical Review A

Concise security bounds for sending-or-not-sending twin-field quantum key distribution with finite pulses

Tingting Song, Peiya Li, Jian Weng

Published Apr 7, 2021• 4 citations
Publisher

Abstract

Since its key rate can overcome the PLOB bound, sending-or-not-sending twin-field quantum key distribution (SNS-TF QKD) schemes attract more and more attention in the past three years. However, the inflection of statistical fluctuations on key rate was not considered quite comprehensively, which blocks the practical application of SNS-TF QKD. We take into account all the statistical fluctuations on probabilities, propose the finite-key analysis for SNS-TF QKD without any assumption on the type of attacks, and obtain the lower bound of key rates by applying an optimizing model. Then the finite-key rates are simulated under the reasonable values of some observed parameters, which shows that the key rates overcome the PLOB bound when the transmission distance is far from 350 km, if the number of pulses is fixed as $N={10}^{14}$. Compared with other SNS-TF QKD schemes, we provide concise and tight finite-key bounds since the statistical fluctuations of all parameters are considered against general attacks.

DOI
10.1103/physreva.103.042408

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Since its key rate can overcome the PLOB bound, sending-or-not-sending twin-field quantum key distribution (SNS-TF QKD) schemes attract more and more attention in the past three years. However, the inflection of statistical fluctuations on key rate was not considered quite comprehensively, which blocks the practical application of SNS-TF QKD. We take into account all the statistical fluctuations on probabilities, propose the finite-key analysis for SNS-TF QKD without any assumption on the type of attacks, and obtain the lower bound of key rates by applying an optimizing model. Then the finite-key rates are simulated under the reasonable values of some observed parameters, which shows that the key rates overcome the PLOB bound when the transmission distance is far from 350 km, if the number of pulses is fixed as N=1014N={10}^{14}N=1014. Compared with other SNS-TF QKD schemes, we provide concise and tight finite-key bounds since the statistical fluctuations of all parameters are considered against general attacks.
Recently, the twin field quantum key distribution (TF-QKD) protocols have been investigated extensively. In particular, an efficient protocol for TF-QKD with sending or not sending the coherent state has been given in. Here in this paper, we present results of practical sending-or-not-sending (SNS) twin field quantum key distribution. In real-life implementations, we need consider the following three requirements, a few different intensities rather than infinite number of different intensities, a phase slice of appropriate size rather than infinitely small size and the statistical fluctuations. We first show the decoy-state method with only a few different intensities and a phase slice of appropriate size. We then give a statistical fluctuation analysis for the decoy-state method. Numerical simulation shows that, the performance of our method is comparable to the asymptotic case for which the key size is large enough. Our method can beat the PLOB bound on secret key capacity. Our results show that practical implementations of the SNS quantum key distribution can be both secure and efficient.
Sending-or-not sending twin-field quantum key distribution (SNS TF-QKD) has the advantage of tolerating large amounts of misalignment errors, and its key rate can exceed the linear bound of repeaterless quantum key distribution. However, the weak randomness in a practical QKD system may lower the secret key rate and limit its achievable communication distance, thus compromising its performance. In this paper, we analyze the effects of the weak randomness on the SNS TF-QKD. The numerical simulation shows that SNS TF-QKD can still have an excellent performance under the weak random condition: the secret key rate can exceed the PLOB boundary and achieve long transmission distances. Furthermore, our simulation results also show that SNS TF-QKD is more robust to the weak randomness loopholes than the BB84 protocol and the measurement-device-independent QKD (MDI-QKD). Our results emphasize that keeping the randomness of the states is significant to the protection of state preparation devices.
Abstract We present a theory for the composable security of sending-or-not-sending (SNS) protocol of twin field quantum key distribution (TF-QKD). We present methods to strictly calculate the finite-key effects in QKD with error rejection through two-way classical communication (TWCC) for SNS TF-QKD protocol. Unlike the normal QKD without TWCC, here the probability of tagging or untagging for each two-bit random group is not independent. We rigorously solve this problem by imagining a virtual set of bits where every bit is independent and identical. With explicit formulas, we show that simply applying Chernoff bound in the calculation gives correct key rate, but the failure probability changes a little bit. We calculate the key rate with strict bounds and security, and obtain key rates by far breaking the PLOB (Pirandola, Laurenza, Ottaviani, and Banchi) bound with composable security.
The twin-field quantum key distribution (TF-QKD) protocol has led to extensive investigation for its capacity of overcoming the rate-distance limit. One variant for TF-QKD named sending-or-not-sending (SNS) TF-QKD has also been proposed. The SNS-TF-QKD encodes the classical keys 0 and 1 in sending or not sending the phase-randomized coherent states, which helps it to tolerate large misalignment errors due to optical phase fluctuations. Nevertheless, the original SNS-TF-QKD scheme utilizes only single-photon interference in generating secret keys, which seems quite different from other TF-QKD protocols. In this paper, we prove that multiphoton interference in the SNS TF-QKD protocol can also contribute to key generation. Accordingly, an improved SNS-TF-QKD scheme with higher key rate is proposed, where events of not only single-photon but also two-photon emissions are considered as effective events.
Twin-field quantum key distribution (TF-QKD), which is immune to all possible detector side channel attacks, enables two remote legitimate users to perform secure communications without quantum repeaters. With the help of a central node, TF-QKD is expected to overcome the linear key-rate constraint using current technologies. However, the security of the former TF-QKD protocols relies on the hypothesis of infinite-key and stable sources. In this paper, we present the finite-key analysis of a practical decoy-state twin-field quantum key distribution with variant statistical fluctuation models. We examine the composable security of the protocol with intensity fluctuations of unstable sources employing Azuma's inequality. Our simulation results indicate that the secret key rate is able to surpass the linear key-rate bound with limited signal pulses and intensity fluctuations. In addition, the effect of intensity fluctuations is extremely significant for small size of total signals.
Twin-field quantum key distribution (TF-QKD) protocol can drastically increase the secure transmission distance of quantum key distribution, changing the channel-loss dependence of key rate fromO(η){O} (\eta)O(η)toO(η){O} (\sqrt {\eta })O(η​). To date, many revolutionary protocols have been invented to increase the practical performances of TF-QKD. However, most of them simply assume using symmetric detectors and ideal beam-splitters, which is inconsistent with the actual experiment. Here, we take experimental imperfections of the detection part in TF-QKD into account, for example, the two detectors own different detection efficiencies, different dark count rates, and the reflectivity of the beam-splitter is unbalanced. We employ the sending-or-not-sending twin-field quantum key distribution (SNS TF-QKD) protocol as an example, constructing a more systematic model to analyze its practical performance. Therefore, our work provides an useful reference for the practical implementation of TF-QKD.