Superadditivity of convex roof coherence measures

TL;DR

This paper investigates the superadditivity property of convex roof coherence measures, providing a theorem to identify which measures are superadditive, and applies it to various known measures to classify their superadditivity.

Contribution

The paper introduces a theorem that offers a sufficient condition for superadditivity of convex roof coherence measures, and applies it to classify several measures.

Findings

Coherence of formation and coherence concurrence are superadditive.

Geometric measure of coherence is non-superadditive.

Convex roof measures based on linear entropy, fidelity, and 1/2-entropy are non-superadditive.

Abstract

In this paper, we examine the superadditivity of convex roof coherence measures. We put forward a theorem on the superadditivity of convex roof coherence measures, which provides a sufficient condition to identify the convex roof coherence measures fulfilling the superadditivity. By applying the theorem to each of the known convex roof coherence measures, we prove that the coherence of formation and the coherence concurrence are superadditive, while the geometric measure of coherence, the convex roof coherence measure based on linear entropy, the convex roof coherence measure based on fidelity, and convex roof coherence measure based on $\frac{1}{2}$-entropy are non-superadditive.