Measure of genuine coherence based of quasi-relative entropy

TL;DR

This paper introduces a new measure of quantum coherence based on quasi-relative entropy, which satisfies key monotonicity properties and provides bounds related to trace distance, advancing the quantification of coherence.

Contribution

It proposes a genuine coherence measure using quasi-relative entropy that is strongly monotone under GIO and offers bounds based on trace distance, improving coherence quantification methods.

Findings

The measure satisfies non-negativity and monotonicity under GIO.

Strong monotonicity holds in low dimensions and for pure states.

Provides bounds on the measure using trace distance.

Abstract

We present a genuine coherence measure based on a quasi-relative entropy as a difference between quasi-entropies of the dephased and the original states. The measure satisfies non-negativity and monotonicity under genuine incoherent operations (GIO). It is strongly monotone under GIO in two- and three-dimensions, or for pure states in any dimension, making it a genuine coherence monotone. We provide a bound on the error term in the monotonicity relation in terms of the trace distance between the original and the dephased states. Moreover, the lower bound on the coherence measure can also be calculated in terms of this trace distance.