Discrete-phase-randomized twin-field quantum key distribution without phase postselection in the test mode

Twin-field quantum key distribution (TF-QKD) can overcome the fundamental rate-loss limit without quantum repeaters, which has stimulated intense research interests both in theory and experiment. Recently, TF-QKD protocols with discrete-phase-randomized sources have been widely studied. However, all these protocols require the phase postselection step in the test mode. To bypass this step, we propose a discrete-phase-randomized TF-QKD protocol without phase postselection in the test mode, which reduces the amount of information transmitted in the classical post-processing stage and thus reduces the consumption of secret keys in the authentication of classical information. Moreover, the numerical simulation of our protocol can be easily solved by linear programming. Simulation results show that, with only a few number of discrete phases, our protocol can beat the rate-loss bound and approximate the case of continuous phases, which is very practical in some real-life implementations of TF-QKD.