Computable measure of quantum correlation

Abstract

A general state of an (formula presented) system is a classical-quantum state if and only if its associated (formula presented)-correlation matrix (a matrix constructed from the coherence vector of the party (formula presented), the correlation matrix of the state, and a function of the local coherence vector of the subsystem (formula presented)), has rank no larger than (formula presented). Using the general Schatten (formula presented)-norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general (formula presented)-norms and any function of the local coherence vector of the unmeasured subsystem, leading to a class of computable quantities which can be used to capture the quantumness of correlations due to the subsystem (formula presented). We introduce two special members of these quantifiers: The first one coincides with the tight lower bound on the geometric measure of discord, so that such lower bound fully captures the quantum correlation of a bipartite system. Accordingly, a vanishing tight lower bound on the geometric discord is a necessary and sufficient condition for a state to be zero-discord. The second quantifier has the property that it is invariant under a local and reversible operation performed on the unmeasured subsystem, so that it can be regarded as a computable well-defined measure of the quantum correlations. The approach presented in this paper provides a way to circumvent the problem with the geometric discord. We provide some examples to exemplify this measure. © 2014, Springer Science+Business Media New York.