Relative state measures of correlations in bipartite quantum systems

TL;DR

This paper introduces geometric measures of total correlation in bipartite quantum systems based on Everett's relative state concept, which are invariant under local unitaries and non-increasing under local operations.

Contribution

It develops a new class of correlation measures derived from the geometric properties of the relative state map, applicable to systems of any dimension.

Findings

Correlation measures are invariant under local unitaries.

Measures are non-increasing under local operations.

Some known correlation measures are interpreted through relative states.

Abstract

Everett's concept of relative state can be viewed as a map that contains information about correlations between measurement outcomes on two quantum systems. We demonstrate how geometric properties of the relative state map can be used to develop operationally well-defined measures of the total correlation in bipartite quantum systems of arbitrary state space dimension. These measures are invariant under local unitary transformations and non-increasing under local operations. We show that some known correlation measures have a natural interpretation in terms of relative states.