Uniform continuity bounds for characteristics of multipartite quantum systems

TL;DR

This paper develops universal methods to establish continuity bounds for key characteristics of multipartite quantum systems, especially in infinite dimensions with energy constraints, ensuring stability of these measures under small perturbations.

Contribution

It introduces new universal techniques for deriving continuity bounds for multipartite quantum characteristics, including mutual information and entanglement measures, in infinite-dimensional settings.

Findings

Continuity bounds for multipartite quantum mutual information are asymptotically tight.

Proved asymptotic continuity of multipartite squashed entanglement and related measures under energy constraints.

Methods applicable to infinite-dimensional quantum systems with energy limitations.

Abstract

We consider universal methods for obtaining (uniform) continuity bounds for characteristics of multipartite quantum systems. We pay a special attention to infinite-dimensional multipartite quantum systems under the energy constraints. By these methods we obtain continuity bounds for several important characteristics of a multipartite quantum state: the quantum (conditional) mutual information, the squashed entanglement, the c-squashed entanglement and the conditional entanglement of mutual information. The continuity bounds for the multipartite quantum mutual information are asymptotically tight for large dimension/energy. The obtained results are used to prove the asymptotic continuity of the $n$-partite squashed entanglement, c-squashed entanglement and the conditional entanglement of mutual information under the energy constraints.