Simple security proof of twin-field type quantum key distribution protocol

Quantum key distribution (QKD) is one of the key applications of the future quantum internet. Nonetheless, optical loss poses fundamental limits [1] for the key rate vs distance performance of secure QKD without trusted relay... [ view full abstract ]

Quantum key distribution (QKD) is one of the key applications of the future quantum internet. Nonetheless, optical loss poses fundamental limits [1] for the key rate vs distance performance of secure QKD without trusted relay nodes. Essentially, these limits state that the key rate scales linearly with the transmittance of the channel.

Remarkably, Lucamarini et al. [2] have recently proposed a novel scheme, called twin-field (TF) QKD, that uses single-photon interference and is conjectured to beat the fundamental bounds in [1]. This has been confirmed by two independent works [3,4], which claim secure key rates that have a square-root improvement over the point-to-point private capacity of an optical QKD link. While this is notable, the security proofs [3,4] are rather complex. Also, both works consider protocols that require post-selection on the matching of the global phase, like in the original TF-QKD proposal.

Inspired by entanglement generation protocols based on single-photon interference in quantum repeaters, here we introduce a conceptually simpler TF-QKD type protocol based on coherent states [5]. See also the independent works [6]. This protocol has two main potential advantages when compared to [2]. First, it does not require a post-selection step based on a global phase matching condition, which might simplify the path to an experimental implementation. And, second, combined with the decoy-state method, it allows the use of the number states as the complementary basis to prove the security, thus leading to a rather simple security proof. 

In so doing, we demonstrate that the secure key rate of our protocol scales as the square-root of the transmittance of the channel, as conjectured by the original TF-QKD scheme. Our results are shown in Fig. 1, where we plot the performance of two variants of our protocol as a function of the overall loss between Alice and Bob.  

[1] M. Takeoka, et al, Nat. Commun. 5, 5235 (2014); S. Pirandola et al., Nat. Commun. 8, 15043 (2017).

[2] M. Lucamarini et al., Nature 557, 400 (2018).

[3] K. Tamaki et al., arXiv:1805.05511. 

[4] X. Ma et al., arXiv:1805.05538.

[5] M. Curty, K. Azuma and H.-K. Lo, arXiv:1807.07667.

[6] C. Cui et al., arXiv:1807.02334; J. Lin et al., arXiv:1807.10202.

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