Unified entropic measures of quantum correlations induced by local measurements

TL;DR

This paper proposes unified entropic measures for quantum correlations that address issues with non-additive entropies, providing a consistent way to quantify quantum correlations in bipartite systems.

Contribution

It introduces a new unified entropic framework for measuring quantum correlations that overcomes previous limitations and recovers known measures as special cases.

Findings

Measures are well-defined for non-additive entropies.

Analytical expressions are derived for typical bipartite systems.

The framework distinguishes total and semiquantum correlations.

Abstract

We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of non-additive entropies. In this way, we overcome the issue of the artificial increasing of the value of quantum correlations measures based on non-additive entropies when an uncorrelated ancilla is appended to the system without changing the computability of our entropic correlations measures with respect to the previous ones. Moreover, we recover as limiting cases the quantum correlations measures based on von Neumann and R\'enyi entropies (i.e., additive entropies), for which the adjustment factor becomes trivial. In addition, we distinguish between total and semiquantum correlations and obtain some relations between them. Finally, we obtain analytical expressions of the entropic correlations measures for typical quantum bipartite systems.