Side-Channel-Secure Quantum Key Distribution with Imperfect Vacuum Sources

Abstract

The side-channel-secure (SCS) quantum key distribution (QKD), SCS QKD has attracted much attention due to its higher security compared to the measurement-device-independent protocols. It is not only measurement-device-independent secure, but also secure against source-state side channels provided that Eve has no access to Alice's or Bob's setups inside their labs. In the original protocol for SCS QKD, the side channels and the intensities of the coherent sources are allowed to be different in different time windows, but the vacuum sources of Alice and Bob have to be perfect, which is impossible in practice due to the finite extinction ratio of the intensity modulators. In this paper, we present a method that does not need the perfect vacuum source requested by the original protocol and assures the result as secure as the original protocol. With the upper bounds of the amplitudes of the nonvacuum part of the sources, the secure key rate of our SCS QKD protocol here with imperfect vacuum and unstable sources can be calculated. The numerical results show that, the secure distance of the SCS QKD protocol exceeds 150 km, provided that the intensity of the imperfect vacuum source is less than ${10}^{\ensuremath{-}8}$, which can be achieved in the experiment by a two-stage intensity modulator, where we also show that the active odd-parity pairing method and standard pairing method using two-way classical communication can be applied to the SCS QKD protocol to improve the key rate. Given the side-channel security based on the existing technological level, this work makes it possible to realize side-channel-secure QKD with real devices.