Finite-key effects in multi-partite quantum key distribution protocols

TL;DR

This paper extends the security analysis of quantum key distribution protocols to multipartite scenarios, deriving key rates considering finite resources and comparing two protocols' performances.

Contribution

It introduces an N-partite version of BB84 and analyzes their security with finite resources, providing computable key rate formulas.

Findings

Derived a computable key rate expression for multipartite protocols.

Compared finite-resource performance of N-partite BB84 and six-state protocols.

Extended bipartite security results to multipartite scenarios.

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 in arXiv:1612.05585v2. 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.