Discord and information deficit in the XX chain

TL;DR

This paper analyzes quantum correlations in the XX spin chain using discord and information deficit, revealing how measurement preferences change with the transverse field and indicating a transition from entangled to separable states.

Contribution

It provides the first exact analysis of quantum discord, geometric discord, and information deficit in the XX chain, highlighting measurement transition phenomena and state changes.

Findings

Quantum discord prefers perpendicular measurements to the field.

Geometric discord and information deficit show a perpendicular to parallel transition.

Transition signals a change from Bell to separable states.

Abstract

We examine the quantum correlations of spin pairs in the cyclic $XX$ spin 1/2 chain in a transverse field, through the analysis of the quantum discord, the geometric discord and the information deficit. It is shown that while these quantities provide the same qualitative information, being non-zero for all temperatures and separations and exhibiting the same type of asymptotic behavior for large temperatures or separations, important differences arise in the minimizing local measurement that defines them. Whereas the quantum discord prefers a spin measurement perpendicular to the transverse field, the geometric discord and information deficit exhibit a perpendicular to parallel transition as the field increases, which subsists at all temperatures and for all separations. Moreover, it is shown that such transition signals the change from a Bell state to an aligned separable state of the dominant eigenstate of the reduced density matrix of the pair. Full exact results for both the thermodynamic limit and the finite chain are provided, through the Jordan-Wigner fermionization.