Ordering states of Tsallis relative $α$-entropies of coherence

In this paper, we study the ordering states with Tsallis relative $α$-entropies of coherence and $l_{1}$ norm of coherence for single-qubit states. We show that any Tsallis relative $α$-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 $α$-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.

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