Finite-key analysis for quantum key distribution with weak coherent pulses based on Bernoulli sampling

Abstract

An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the BB84 protocol with weak coherent pulses, reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also applied the method to prove the security of the differentialquadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that, the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.

Quantum key distribution with setting-choice-independently correlated light sources

“…In the simulation, we assume that Bob uses a measurement setup with two single-photon detectors with detection efficiency η det = 10% and dark count probability per pulse p dark = 10 −5 . These parameters are set to be the same as those in [43]. The attenuation coefficient of the optical fibre is 0.2 dB/km and its transmittance is η ch = 10 −0.2l/10 with l denoting the fibre length.…”