Computable measure of quantum correlation.

Akhtarshenas, S.; Mohammadi, Hamidreza; Karimi, Saman; Azmi, Zahra

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.

QUANTUM correlations; QUANTUM entanglement; QUANTUM coherence; QUANTUM states; MATHEMATICAL bounds

Quantum Information Processing, 2015, Vol 14, Issue 1, p247

1570-0755

Academic Journal

10.1007/s11128-014-0839-2