Correlations in quantum states and the local creation of quantum discord

TL;DR

This paper offers a new perspective on quantum correlations by linking quantum discord to the rank of the correlation matrix, highlighting that discord indicates quantumness rather than the total quantum correlations.

Contribution

It introduces an alternative view on quantum correlations based on the correlation matrix rank and clarifies the relationship between quantum discord and quantum correlations.

Findings

Quantum discord relates to the quantumness of states, not total quantum correlations.

States with nonzero discord can be generated from zero discord states via local operations.

The set of states created by local operations from zero discord states has measure zero.

Abstract

Quantum discord is usually referred to as a measure for quantum correlations. In the search of the fundamental resource to gain a quantum advantage in quantum information applications, quantum discord is considered a promising candidate. In this paper we present an alternative view on quantum correlations in terms of the rank of the correlation matrix as introduced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)]. According to our analysis, information about the quantum discord does not necessarily determine the amount of quantum correlations but rather the quantumness of the state. Nonzero quantum discord is only a necessary but not a sufficient condition for correlations above the classically achievable limit. This becomes clear when we consider states of nonzero discord, which can be created from zero discord states only by a single local operation. We further show that the set of these states has measure zero.