Uniform Additivity of Tripartite Optimized Correlation Measures

TL;DR

This paper identifies conditions under which certain tripartite quantum correlation measures are additive, simplifying the computation of optimal quantum communication rates by leveraging entropy properties.

Contribution

It extends the concept of uniform additivity from bipartite to tripartite quantum correlation measures, providing a framework for tractable evaluation of these measures.

Findings

Identified convex cones of uniformly additive tripartite measures.

Proved additivity of three previously known tripartite correlation measures.

Utilized strong subadditivity to establish additivity results.

Abstract

Information theory provides a framework for answering fundamental questions about the optimal performance of many important quantum communication and computational tasks. In many cases, the optimal rates of these tasks can be expressed in terms of regularized formulas that consist of linear combinations of von Neumann entropies optimized over state extensions. However, evaluation of regularized formulas is often intractable, since it involves computing a formula's value in the limit of infinitely many copies of a state. To find optimized, linear entropic functions of quantum states whose regularized versions are tractable to compute, we search for linear combinations of entropies on tripartite quantum states that are additive. We use the method of \cite{cross2017uniform}, which considers bipartite formulas, to identify convex polyhedral cones of uniformly additive \emph{tripartite} correlation measures. We rely only on strong subadditivity of the von Neumann entropy and use these cones to prove that three previously established tripartite optimized correlation measures are additive.