Quantum Correlations in Large-Dimensional States of High Symmetry

TL;DR

This paper analyzes quantum correlations in high-dimensional Werner and pseudo-pure states, deriving explicit formulas for quantum discord and related measures, revealing contrasting behaviors in classical and quantum correlations as dimensions grow.

Contribution

It provides closed-form expressions for quantum discord and related measures in Werner and pseudo-pure states, and verifies a conjecture relating geometric discord and negativity.

Findings

Quantum correlations in Werner states remain bounded and independent of entanglement in high dimensions.

Pseudo-pure states show unbounded growth of quantum and classical correlations with increasing dimension.

Pseudo-pure states satisfy the conjecture that geometric discord upper bounds squared negativity.

Abstract

In this article, we investigate how quantum correlations behave for the so-called Werner and pseudo-pure families of states. The latter refers to states formed by mixing any pure state with the totally mixed state. We derive closed expressions for the Quantum Discord (QD) and the Relative Entropy of Quantumness (REQ) for these families of states. For Werner states, the classical correlations are seen to vanish in high dimensions while the amount of quantum correlations remain bounded and become independent of whether or not the the state is entangled. For pseudo-pure states, nearly the opposite effect is observed with both the quantum and classical correlations growing without bound as the dimension increases and only as the system becomes more entangled. Finally, we verify that pseudo-pure states satisfy the conjecture of [\textit{Phys. Rev. A} \textbf{84}, 052110 (2011)] which says that the Geometric Measure of Discord (GD) always upper bounds the squared Negativity of the state.