Practical decoy-state method for twin-field quantum key distribution

Abstract

Twin-field (TF) quantum key distribution (QKD) represents a novel QKD approach whose principal merit is to beat the point-to-point private capacity of a lossy quantum channel, thanks to performing single-photon interference in an untrusted node. Indeed, recent security proofs of various TF-QKD type protocols have confirmed that the secret key rate of these schemes scales essentially as the square root of the transmittance of the channel. Here, we focus on the TF-QKD protocol introduced by Curty et al, whose secret key rate is nearly an order of magnitude higher than previous solutions. Its security relies on the estimation of the detection probabilities associated to various photon-number states through the decoy-state method. We derive analytical bounds on these quantities assuming that each party uses either two, three or four decoy intensity settings, and we investigate the protocol's performance in this scenario. Our simulations show that two decoy intensity settings are enough to beat the point-to-point private capacity of the channel, and that the use of four decoys is already basically optimal, in the sense that it almost reproduces the ideal scenario of infinite decoys. We also observe that the protocol seems to be quite robust against intensity fluctuations of the optical pulses prepared by the parties.The last few decades have witnessed major advancements in the field of quantum communication [1, 2], with quantum key distribution (QKD) [3-13] being its most developed application. Recent experiments over about 400 km of optical fibers [14,15] and over about 1000 km of satellite-to-ground links [16,17] demonstrated that QKD over long distances is possible. Despite such remarkable experimental achievements, the private capacity of point-to-point QKD is intrinsically limited by fundamental bounds [18,19]. These bounds state that in the high-loss regime the key rate scales basically linearly with the transmittance of the channel connecting the endusers Alice and Bob, i.e. it decreases exponentially with the total channel length. This imposes strict practical constraints on the possibility of achieving point-to-point QKD over arbitrary long distances.A way to overcome this limitation is to employ one or more intermediate nodes in the quantum channel connecting the parties. For instance, the use of quantum repeaters [20] yields a polynomial scaling of the communication efficiency with the distance [21]. Moreover, a quantum repeater scheme can be arbitrarily iterated along the quantum channel, thus increasing in principle the total communication distance between Alice and Bob as much as desired. Unfortunately, however, quantum repeaters are very challenging to build in practice with current technology: they either require quantum memories [20][21][22] or quantum error correction [23,24]. Of course, technology is improving, and quantum repeaters may become viable in the future.Other solutions, which attain a square-root improvement in the scaling of the key rate with respect to the transmittance of the channel, ...

Practical issues of twin-field quantum key distribution

“…Note added-Recently, we found that [51,52] discussed the finite-key size effect and [53,54] discussed the security of TF-QKD under intensity fluctuation.…”

Asymmetric twin-field quantum key distribution

“…This is clear from figure 2, where we plot the secret key rate assuming that Alice and Bob use the same set of two, three and four decoy intensities. The plots are obtained by using the analytical yields bounds for the symmetric-intensities scenario derived in [28]. The experimental parameters used for the simulations are given in table 1 and the corresponding channel model is given in appendix A.…”

“…Moreover, the practical feasibility of this scheme has been recently demonstrated in [24,25,27]. A complete analysis of the symmetric scenario where both users use the same signal intensities and analytically estimate the yields using the same decoy intensity settings was performed recently in [28]. However, using the same set of intensities is an optimal strategy only when the quantum channels connecting the users to the central node have approximately the same transmittance.…”

“…However, using the same set of intensities is an optimal strategy only when the quantum channels connecting the users to the central node have approximately the same transmittance. Thus, the bounds derived in [28] are not suitable for several real-world situations in optical networks where the distances between the users and the central node can be notoriously different. Furthermore, assuming that the parties employ exactly the same intensities is problematic even when the losses are symmetric.…”

Conference key agreement with single-photon interference

“…reducing the assumption on the devices) [9-14], but at the same time are also implementable with today's technology [15][16][17][18]. In this context, a protocol which recently received great attention is the Twin-Field (TF) QKD protocol originally proposed by Lucamarini et al [19], further developed to prove its security [20][21][22][23][24][25][26][27] and experimentally implemented [28][29][30][31]. Indeed, the TF-QKD protocol relies only on single-photon interference occurring in an untrusted node, making it a measurement-device-independent (MDI) QKD protocol capable of overcoming the repeaterless bounds [32,33].In a scenario where several users are required to share a common secret key, one can for instance perform bipartite QKD protocols between pairs of users and then use the secret keys established in this way to encode the final common secret key.…”