General quantum correlation from nonreal values of Kirkwood-Dirac quasiprobability over orthonormal product bases

TL;DR

This paper introduces a new measure of quantum correlation based on the nonreal values of Kirkwood-Dirac quasiprobability, applicable even to unentangled states, with implications for quantum information processing.

Contribution

It proposes a novel quantification method for general quantum correlations using KD quasiprobability, extending beyond entanglement and linking to quantum uncertainty and nonlocality.

Findings

The measure provides a lower bound to quantum uncertainty in local measurements.

It acts as a faithful witness for entanglement and measurement-induced nonlocality.

A variational scheme for estimating the measure is discussed.

Abstract

We propose a characterization and a quantification of general quantum correlation which is exhibited even by a separable (unentangled) mixed bipartite state in terms of the nonclassical values of the associated Kirkwood-Dirac (KD) quasiprobability. Such a general quantum correlation, wherein entanglement is a subset, is not only intriguing from a fundamental point of view, but it has also been recognized as a resource in a variety of schemes of quantum information processing and quantum technology. Given a bipartite state, we construct a quantity based on the imaginary part the associated KD quasiprobability defined over a pair of orthonormal product bases and an optimization procedure over all pairs of such bases. We show that it satisfies certain requirements expected for a quantifier of general quantum correlations. It gives a lower bound to the total sum of the quantum standard deviation of all the elements of the product (local) basis, minimized over all such bases. It suggests an interpretation as the minimum genuine quantum share of uncertainty in all possible local von-Neumann projective measurement. Moreover, it is a faithful witness for entanglement and measurement-induced nonlocality of pure bipartite states. We then discuss a variational scheme for its estimation, and based on this, we offer information theoretical meanings of the general quantum correlation. Our results suggest a deep connection between the general quantum correlation and the nonclassical values of the KD quasiprobability and the associated strange weak values.