Finite-key effects in multipartite quantum key distribution protocols

Abstract

We analyze the security of two multipartite quantum key distribution (QKD) protocols, specifically we introduce an N-partite version of the BB84 protocol and we discuss the N-partite six-state protocol proposed by Epping et al (2017 New J. Phys. 19 093012). The security analysis proceeds from the generalization of known results in bipartite QKD to the multipartite scenario, and takes into account finite resources. In this context we derive a computable expression for the achievable key rate of both protocols by employing the best-known strategies: the uncertainty relation and the postselection technique. We compare the performances of the two protocols both for finite resources and infinitely many signals.