Twin field quantum key distribution promises high key rates at long distance to beat the rate distance limit. Here, applying the sending or not sending TF QKD protocol, we experimentally demonstrate a secure key distribution breaking the absolute key rate limit of repeaterless QKD over 509 km, 408 km ultra-low loss optical fibre and 350 km standard optical fibre. Two independent lasers are used as the source with remote frequency locking technique over 500 km fiber distance; Practical optical fibers are used as the optical path with appropriate noise filtering; And finite key effects are considered in the key rate analysis. The secure key rates obtained at different distances are more than 5 times higher than the conditional limit of repeaterless QKD, a bound value assuming the same detection loss in the comparison. The achieved secure key rate is also higher than that a traditional QKD protocol running with a perfect repeaterless QKD device and even if an infinite number of sent pulses. Our result shows that the protocol and technologies applied in this experiment enable TF QKD to achieve high secure key rate at long distribution distance, and hence practically useful for field implementation of intercity QKD.Introduction.-Channel loss seems to be the most severe limitation on the practical application of long distance quantum key distribution (QKD) [1-3], given that quantum signals cannot be amplified. Much efforts have been made towards the goal of a longerdistance for QKD [4][5][6]. Theoretically, the decoy-state method [7][8][9] can improve the key rate of coherent-state based QKD from scaling quadratically to a linear with the channel transmittance, as what behaves of a perfect single-photon source. This method can beat the photonnumber-splitting attack to the imperfect single-photon source and the coherent state is used as if only those single-photon pulses were used for key distillation, and hence it can reach the key rate to a level comparable with that of a perfect single-photon source.

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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.

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Odd-parity error rejection (OPER), in particular the method of actively odd parity pairing (AOPP), can drastically improve the asymptotic key rate of sending-or-not-sending twin-field (SNS-TF) quantum key distribution (QKD). However, in practice, the finite-key effects have to be considered for the security. Here, we propose a zigzag approach to verify the phase-flip error of the survived bits after OPER or AOPP. Based on this, we can take all the finite-key effects efficiently in calculating the non-asymptotic key rate. Numerical simulation shows that our approach here produces the highest key rate over all distances among all existing methods, improving the key rate by more than 100% to 3000% in comparison with different prior art methods with typical experimental setting. These verify the advantages of the AOPP method with finite data size. Also, with our zigzag approach here, the non-asymptotic key rate of SNS-TF QKD can by far break the absolute bound of repeater-less key rate with whatever detection efficiency. We can even reach a non-asymptotic key rate more than 40 times of the practical bound and 13 times of the absolute bound with 10 12 pulses. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische GesellschaftNew J. Phys. 22 (2020) 053048 C Jiang et al [73][74][75]. More precisely, we show that is able to beat the repeater-less PLOB bound [75] established by Pirandola, Laurenza, Ottaviani, and Banchi, which is the fundamental benchmark used in the literature. Experiments [76][77][78][79][80][81] have been done to demonstrate those protocols. In particular, the efficient variant of TF QKD, named sending-or-not-sending (SNS) protocol has been proposed in reference [12]. The SNS protocol has its advantage of tolerating large misalignment errors [12,18] and unconditional security with finite key size [21]. The numerical results show that the secure distance can exceed 500 km even when the misalignment error is as large as 20% [21]. The SNS protocol has been experimentally demonstrated in proof-of-principle in reference [76], and realized in real optical fiber with the finite-key effects taken into consideration [77,80]. Based on the idea of SNS, long distance side-channel-free QKD was proposed recently [9], using coherent states only.However, there are still considerable spaces to further improve the performance of the SNS protocol. For example, the original SNS protocol [12,18,21] is limited to small probability of sending a signal coherent state and this limits its key rate.There are several methods proposed in reference [22] to improve the key rate of SNS protocol, such as the standard error rejection and odd-parity error rejection (OPER) including the method of actively odd parity pairing (AOPP) with infinite key size. Among all those methods, the numerical results show that the OPER, especially the AOPP methods can drastically improve the key rate and secure distance of SNS protocol with infinite key size. But to show the advantage of OPE...