Tight finite-key analysis for mode-pairing quantum key distribution

Mode-pairing quantum key distribution (MP-QKD) is a potential protocol that is not only immune to all possible detector side channel attacks, but also breaks the repeaterless rate-transmittance bound without needing global phase locking. Here we analyze the finite-key effect for the MP-QKD protocol with rigorous security proof against general attacks. Moreover, we propose a six-state MP-QKD protocol and analyze its finite-key effect. The results show that the original protocol can break the repeaterless rate-transmittance bound with a typical finite number of pulses in practice. And our six-state protocol can improve the secret key rate significantly in long distance cases.