Ordering states of Tsallis relative $\alpha$-entropies of coherence

Abstract

In this paper, we study the ordering states with Tsallis relative $\alpha$-entropies of coherence and $l_1$ norm of coherence for single-qubit states. We show that any Tsallis relative $\alpha$-entropies of coherence and $l_1$ norm of coherence give the same ordering for single-qubit pure states. However, they don't generate the same ordering for some high dimensional pure states, even though these states are pure. We also consider three special Tsallis relative $\alpha$-entropies of coherence, such as $C_1$ ,$C_2$ and $C_{\frac{1}{2}}$, and show any one of these three measures and $C_{l_1}$ will not generate the same ordering for single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states.