Quantum average correlation based on average coherence

TL;DR

This paper introduces a quantum average correlation measure based on average coherence, exploring its properties, equivalences, and relation to wave-particle duality in bipartite systems.

Contribution

It defines a new quantum correlation measure using two equivalent approaches and proves its key properties and connections to wave-particle duality.

Findings

The correlation measure is non-negative, contractive, and invariant under local unitaries.

The two approaches to defining average coherence are mathematically equivalent.

A complementarity relation links wave-particle duality with the average correlation.

Abstract

This paper studies the quantification and structural properties of quantum average correlation based on average coherence. Motivated by two mathematically equivalent approaches to define average coherence: one by averaging over complete sets of mutually unbiased bases, and the other by integrating over all orthogonal bases under the Haar measure, we define an average correlation for bipartite systems as the difference between global and local skew information. This correlation measure is shown to satisfy essential properties including non negativity, contractivity under local quantum channels, and local unitary invariance. We further prove the equivalence between the average correlation defined via mutually unbiased bases and that defined via unitary groups. Finally, we derive a complementarity relation that connects wave-particle duality with the average correlation between a system and its environment.