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

Abstract

We propose a characterization and a quantification of the 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 the 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 possible 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 possible of such bases. It suggests an interpretation as the minimum genuine quantum share of uncertainty in all local von-Neumann projective measurement. Moreover, it is a faithful witness for entanglement and measurement-induced nonlocality of general pure bipartite states. We then discuss the general scheme for its measurement, 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.

Resource theory of Kirkwood-Dirac imaginarity

“…{| } of the Hilbert space of a quantum system, the Kirkwood-Dirac distribution (KDD) of a quantum state ρ was defined as ), it is also called KD quasiprobability and becomes an extension of classical probability distribution. According to the positivity of the KDD, quantum states are divided into KD-classical and KD-nonclassical ones in the previous works [23,25,29,31,32,56,61].…”

“…This special QPD Q AB (ρ) is named the Kirkwood-Dirac distribution (KDD), or the Kirkwood-Dirac quasiprobability (KDQ), which was proposed by Kirkwood [21] and Dirac [22] independently. Recently, it has been proved that nonclassical values (negative and non-real values) of KDQ Q AB (ρ) have the ability of outperforming their classical counterparts in quantum computation, quantum measurement and thermodynamics [23][24][25][26][27][28][29][30][31][32].…”