Quantum Discord and entropic measures of quantum correlations: Optimization and behavior in finite $XY$ spin chains

TL;DR

This paper explores generalized entropic measures of quantum correlations, such as quantum discord and information deficit, in finite XY spin chains, revealing their behavior near factorizing fields and differences in optimal measurements.

Contribution

It introduces a formalism for generalized entropic measures that simplifies optimization in qudit-qubit systems and applies it to analyze quantum correlations in XY spin chains.

Findings

Quantum discord and information deficit show similar behavior in spin chains.

Optimal measurements for these quantities differ significantly.

Quantum correlations exhibit notable features near factorizing fields.

Abstract

We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the associated optimization problem in qudit-qubit systems is shown to become feasible, allowing to approximate that of the quantum discord. As application, we examine quantum correlations of spin pairs in the exact ground state of finite $XY$ spin chains in a magnetic field through the quantum discord and information deficit. While these quantities show a similar behavior, their optimizing measurements exhibit significant differences, which can be understood and predicted through the previous approximations. The remarkable behavior of these quantities in the vicinity of transverse and non-transverse factorizing fields is also discussed.