Information complementarity in multipartite quantum states and security in cryptography

TL;DR

This paper establishes complementarity relations between purity and various correlations in multipartite quantum states and applies these to bound secret key rates in quantum cryptography.

Contribution

It introduces general complementarity relations for multipartite quantum states and uses them to derive bounds on secret key rates in quantum cryptography.

Findings

Complementarity relations between purity and correlations in multipartite states.

Bound on secret key rate for individual attacks in quantum key distribution.

Applicable to systems of arbitrary size and dimensions.

Abstract

We derive complementarity relations for arbitrary quantum states of multiparty systems, of arbitrary number of parties and dimensions, between the purity of a part of the system and several correlation quantities, including entanglement and other quantum correlations as well as classical and total correlations, of that part with the remainder of the system. We subsequently use such a complementarity relation, between purity and quantum mutual information in the tripartite scenario, to provide a bound on the secret key rate for individual attacks on a quantum key distribution protocol.