Non-commutative measure of quantum correlations under local operations
arXiv:1808.03131 · doi:10.1007/s11128-018-2154-9
Abstract
We study some desirable properties of recently introduced measures of quantum correlations based on the amount of non-commutativity quantified by the Hilbert-Schmidt norm (Sci Rep 6:25241, 2016, and Quantum Inf. Process. 16:226, 2017). Specifically, we show that: 1) for any bipartite () state, the measures of quantum correlations with respect to subsystem are non-increasing under any Local Commutative Preserving Operation on subsystem , and 2) for Bell diagonal states, the measures are non-increasing under arbitrary local operations on . Our results accentuate the potentialities of such measures, and exhibit them as valid monotones in a resource theory of quantum correlations with free operations restricted to the appropriate local channels.
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