Oblique discord

TL;DR

This paper introduces oblique discord, a new quantum correlation measure that generalizes quantum discord by relaxing the orthogonality condition, and explores its properties, geometric measure, and potential extensions.

Contribution

It defines oblique discord, characterizes zero-oblique-discord states, and proposes a geometric measure, expanding the understanding of quantum correlations beyond entanglement and discord.

Findings

Zero-oblique-discord states include more states than zero-discord states.

A geometric measure for oblique discord is proposed.

Conjecture on information-theoretic measure for oblique discord is raised.

Abstract

Discord and entanglement characterize two kinds of quantum correlations, and discord captures more correlation than entanglement in the sense that even separable states may have nonzero discord. In this paper, we propose a new kind of quantum correlation we call it oblique discord. A zero-discord state corresponds to an orthonormal basis, while a zero-oblique-discord state corresponds to a basis which is not necessarily orthogonal. Under this definition, the set of zero-discord states is properly contained inside the set of zero-oblique-discord states, and the set of zero-oblique-discord states is properly contained inside the set of separable states. We give a characterization of zero-oblique-discord states via quantum operation, provide a geometric measure for oblique discord, and raise a conjecture with it holds we can define an information-theoretic measure for oblique discord. Also, we point out that, the definition of oblique discord can be properly extended to some different versions just as the case of quantum discord.