Negativity of quantumness and its interpretations

TL;DR

This paper investigates the negativity of quantumness as a measure of nonclassical correlations in quantum systems, providing interpretations, calculations for specific states, and discussing its significance in quantum information processing.

Contribution

It offers a comprehensive analysis of negativity of quantumness, including geometric and operational interpretations, and derives closed-form expressions for key quantum states.

Findings

Negativity of quantumness has a geometric interpretation as minimum trace distance.

Closed-form formulas are derived for Werner, isotropic, and Bell diagonal states.

The measure's operational significance in quantum information tasks is discussed.

Abstract

We analyze the general nonclassicality of correlations of a composite quantum systems as measured by the negativity of quantumness. The latter corresponds to the minimum entanglement, as quantified by the negativity, that is created between the system and an apparatus that is performing local measurements on a selection of subsystems. The negativity of quantumness thus quantifies the degree of nonclassicality on the measured subsystems. We demonstrate a number of possible different interpretations for this measure, and for the concept of quantumness of correlations in general. In particular, for general bipartite states in which the measured subsystem is a qubit, the negativity of quantumness acquires a geometric interpretation as the minimum trace distance from the set of classically correlated states. This can be further reinterpreted as minimum disturbance, with respect to trace norm, due to a local measurement or a nontrivial local unitary operation. We calculate the negativity of quantumness in closed form for Werner and isotropic states, and for all two-qubit states for which the reduced state of the system that is locally measured is maximally mixed---this includes all Bell diagonal states. We discuss the operational significance and potential role of the negativity of quantumness in quantum information processing.