Oblique discord

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 that we call as 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 mapping, provide a geometric measure for oblique discord, and raise a conjecture, which if it holds, then 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.