Quantum average correlations and complementarity relations via metric-adjusted skew information

TL;DR

This paper introduces a unified framework for quantum average correlations and complementarity relations using metric-adjusted skew information, applicable across various averaging schemes.

Contribution

It derives a closed-form expression for average correlations that is independent of the averaging method, linking wave-particle features, entropy, and correlations.

Findings

Derived a universal expression for average correlations.

Established complementarity relations among wave, particle features, and entropy.

Unified different averaging procedures under a common framework.

Abstract

We investigate quantum average correlations and complementarity relations based on metric-adjusted skew information. Several natural averaging procedures are considered, including complete families of mutually unbiased bases, all orthonormal bases, operator orthonormal bases, and twirling channels induced by the unitary group. All these approaches lead to the same closed expression, which identifies the resulting average correlation as an intrinsic quantity independent of the averaging scheme. By defining measures of wave and particle features via metric-adjusted skew information, we establish complementarity relations among wave and particle features, quantum entropy, and average correlation. These results provide a unified framework for investigating quantum average correlations and complementarity relations in terms of metric-adjusted skew information.