Quantum discord of ensemble of quantum states

TL;DR

This paper explores the relationship between quantum discord and accessible information in quantum ensembles, providing new insights and methods for evaluating quantum correlations and their implications for quantum information processing.

Contribution

It introduces an information-theoretic interpretation of quantum discord, relates it to accessible information, and extends existing results to mixed states using quantum discord perspective.

Findings

Quantum discord equals the gap between accessible information and the Holevo bound.

Koashi-Winter relation simplifies the evaluation of quantum discord for pure states.

Geometric discord serves as an effective indicator of quantumness in ensembles.

Abstract

We highlight an information-theoretic meaning of quantum discord as the gap between the ac- cessible information and the Holevo bound in the framework of ensemble of quantum states. This complementary relationship implies that a large amount of pre-existing arguments about the evaluation of quantum discord can be directly applied to the accessible information and vice versa. For an ensemble of two pure qubit states, we show that one can evade the optimization problem with the help of the Koashi-Winter relation. Further, for the general case (two mixed qubit states), we recover the main results presented by Fuchs and Caves [Phys. Rev. Lett. 73, 3047 (1994)], but totally from the perspective of quantum discord. Following this line of thought, we also investigate the geometric discord as an indicator of quantumness of ensembles in detail. Finally, we give an example to elucidate the difference between quantum discord and geometric discord with respect to optimal measurement strategies.