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arXiv · 1607.01591

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

Fu-Gang Zhang·Lian-He Shao·Yu Luo·Yongming Li
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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.

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Fu-Gang Zhang, Lian-He Shao, Yu Luo, Yongming Li. 2016-07-06. Ordering states of Tsallis relative $\alpha$-entropies of coherence. https://arxiv.org/abs/1607.01591

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