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arXiv · 1808.03131

Non-commutative measure of quantum correlations under local operations

D. G. Bussandri·A. P. Majtey·A. Valdés-Hernández
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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 ($A+B$) state, the measures of quantum correlations with respect to subsystem $A$ are non-increasing under any Local Commutative Preserving Operation on subsystem $A$, and 2) for Bell diagonal states, the measures are non-increasing under arbitrary local operations on $B$. 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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D. G. Bussandri, A. P. Majtey, A. Valdés-Hernández. 2019-02-25. Non-commutative measure of quantum correlations under local operations. https://doi.org/10.1007/s11128-018-2154-9

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