Measure of genuine coherence based of quasi-relative entropy

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 under GIO 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.

Automated summary

In this paper, a genuine coherence measure based on a quasi-relative entropy is presented. The measure satisfies non-negativity and monotonicity under genuine incoherent operations. It is strongly monotone under such operations in two and three dimensions, or for pure states in any dimension, making it a genuine coherence monotone. The paper also provides a bound on the error term in the monotonicity relation under genuine incoherent operations, which can be expressed in terms of the trace distance between the original and the dephased states.