Quantum discord and information deficit in spin chains

TL;DR

This paper investigates quantum correlations in spin chains using quantum discord and information deficits, revealing their behavior in ground states and differences from entanglement, with analytical and numerical insights.

Contribution

It introduces a unified analysis of quantum discord and information deficits in spin chains, highlighting their behavior near critical and factorizing fields, and compares them to entanglement.

Findings

Quantum correlations extend over full range near the factorizing field.

Quantum discord and information deficits differ in their local measurement optimizations.

Correlations persist in separable states, unlike entanglement.

Abstract

We examine the behavior of quantum correlations of spin pairs in a finite anisotropic $XY$ spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one way-information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.