A New Quantum Data Processing Inequality

TL;DR

This paper introduces a non-additive measure called maximal correlation for bipartite quantum states, establishing a new data processing inequality that bounds state transformations even with unlimited copies of the resource.

Contribution

It proposes the maximal correlation measure and proves a data processing inequality for it, providing bounds on state transformations in quantum information processing.

Findings

Maximal correlation is non-additive and consistent across multiple copies.

A new data processing inequality for maximal correlation is established.

Boundaries on state transformations under local operations are derived.

Abstract

Quantum data processing inequality bounds the set of bipartite states that can be generated by two far apart parties under local operations; Having access to a bipartite state as a resource, two parties cannot locally transform it to another bipartite state with a mutual information greater than that of the resource state. But due to the additivity of quantum mutual information under tensor product, the data processing inequality gives no bound when the parties are provided with arbitrary number of copies of the resource state. In this paper we introduce a measure of correlation on bipartite quantum states, called maximal correlation, that is not additive and gives the same number when computed for multiple copies. Then by proving a data processing inequality for this measure, we find a bound on the set of states that can be generated under local operations even when an arbitrary number of copies of the resource state is available.