Computable measure of the quantum correlation

Abstract

A general state of an $m\otimes n$ system is a classical-quantum state if and only if its associated $A$-correlation matrix (a matrix constructed from the coherence vector of the party $A$, the correlation matrix of the state, and a function of the local coherence vector of the subsystem $B$), has rank no larger than $m-1$. Using the general Schatten $p$-norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general $p$-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 $A$. 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.

14 pages, Title and Abstract are changed, Sections I, III are modified, Two figures are added, Appendices A and B are added, Conclusion is refined

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• Measuring quantum discord using the most distinguishable steered states
• Computable Measure of Total Quantum Correlation of Multipartite Systems