Entanglement and quantum correlations in many-body systems: a unified approach via local unitary operations

TL;DR

This paper introduces a unified approach using local unitary operations to quantify quantum correlations, comparing entanglement and discord in many-body systems like XY spin chains across different states and temperatures.

Contribution

It develops a unified framework for quantifying quantum correlations via local unitaries and applies it to analyze entanglement and discord in infinite spin chains.

Findings

Quantum discord dominates entanglement in symmetry-preserving ground states.

Quantum discord is suppressed in symmetry-breaking ground states, while entanglement remains stable.

Both quantum discord and entanglement can increase with temperature in certain regimes.

Abstract

Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum system. For pure states, the distance between a given state and its image under least-perturbing local unitary operations is a bona fide measure of quantum entanglement, the so-called entanglement of response, which can be extended to mixed states via the convex roof construction. On the other hand, when defined directly on mixed states perturbed by local unitary operations, such a distance turns out to be a bona fide measure of quantum correlations, the so-called discord of response. Exploiting this unified framework, we perform a detailed comparison between two-body entanglement and two-body quantum discord in infinite XY quantum spin chains both in symmetry-preserving and symmetry-breaking ground states as well as in thermal states at finite temperature. The results of the investigation show that in symmetry-preserving ground states the two-point quantum discord dominates over the two-point entanglement, while in symmetrybreaking ground states the two-point quantum discord is strongly suppressed and the two-point entanglement is essentially unchanged. In thermal states, for certain regimes of Hamiltonian parameters, we show that the pairwise quantum discord and the pairwise entanglement can increase with increasing thermal fluctuations.