Finite-key security against coherent attacks in quantum key distribution

TL;DR

This paper extends finite-key security analysis to coherent attacks in quantum key distribution, applying it to a protocol with unmonitored, varying reference frames, emphasizing the importance of finite-key considerations for practical security.

Contribution

It explicitly derives finite-key bounds for unconditional security against coherent attacks and applies these bounds to a protocol with unmonitored reference frame alignment.

Findings

Finite-key bounds are derived for protocols under coherent attacks.

The analysis shows the importance of finite-key effects in practical scenarios.

Optimal number of signals for secure key generation is identified.

Abstract

The work by Christandl, K\"onig and Renner [Phys. Rev. Lett. 102, 020504 (2009)] provides in particular the possibility of studying unconditional security in the finite-key regime for all discrete-variable protocols. We spell out this bound from their general formalism. Then we apply it to the study of a recently proposed protocol [Laing et al., Phys. Rev. A 82, 012304 (2010)]. This protocol is meaningful when the alignment of Alice's and Bob's reference frames is not monitored and may vary with time. In this scenario, the notion of asymptotic key rate has hardly any operational meaning, because if one waits too long time, the average correlations are smeared out and no security can be inferred. Therefore, finite-key analysis is necessary to find the maximal achievable secret key rate and the corresponding optimal number of signals.