Quantifying Nonclassicality of Correlations based on the Concept of Nondisruptive Local State Identification

TL;DR

This paper introduces a new family of quantum correlation measures based on the concept of nondisruptive local state identification, utilizing Schatten p-norms to quantify nonclassicality and exploring their properties and relation to entanglement.

Contribution

It proposes a novel class of quantum correlation measures using Schatten p-norms, including a closed-form for p=2, and establishes their properties and connection to entanglement.

Findings

Measures are reliable from an information theoretic perspective.

Monotonicity under LOCC demonstrated for these measures.

Upper bounds relate to entanglement monotones, enabling a new entanglement measure.

Abstract

A bipartite state is classical with respect to party $A$ if and only if party $A$ can perform nondisruptive local state identification (NDLID) by a projective measurement. Motivated by this we introduce a class of quantum correlation measures for an arbitrary bipartite state. The measures utilize the general Schatten $p$-norm to quantify the amount of departure from the necessary and sufficient condition of classicality of correlations provided by the concept of NDLID. We show that for the case of Hilbert-Schmidt norm, i.e. $p=2$, a closed formula is available for an arbitrary bipartite state. The reliability of the proposed measures is checked from the information theoretic perspective. Also, the monotonicity behavior of these measures under LOCC is exemplified. The results reveal that for the general pure bipartite states these measures have an upper bound which is an entanglement monotone in its own right. This enables us to introduce a new measure of entanglement, for a general bipartite state, by convex roof construction. Some examples and comparison with other quantum correlation measures are also provided.