A general state of an $$m\otimes n$$ m ⊗ n system is a classical-quantum state if and only if its associated $$A$$ A -correlation matrix (a matrix constructed from the coherence vector of the party $$A$$ A , the correlation matrix of the state, and a function of the local coherence vector of the subsystem $$B$$ B ), has rank no larger than $$m-1$$ m - 1 . Using the general Schatten $$p$$ p -norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general $$p$$ 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 $$A$$ 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.
Quantum Information Processing – Springer Journals
Published: Oct 7, 2014
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