Non-commutative measure of quantum correlations under local operations

TL;DR

This paper investigates properties of quantum correlation measures based on non-commutativity, demonstrating their monotonicity under specific local operations, thus supporting their role as valid resource quantifiers in quantum information theory.

Contribution

It establishes that these non-commutative measures are non-increasing under certain local operations, confirming their validity as monotones in quantum resource theories.

Findings

Measures are non-increasing under local commutative preserving operations on subsystem A.

Measures are non-increasing under arbitrary local operations on Bell diagonal states.

Supports the use of these measures as valid monotones in quantum resource theories.

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.