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

Abstract

In this paper, we study the ordering states with Tsallis relative $$\alpha $$?-entropies of coherence and $$l_{1}$$l1 norm of coherence for single-qubit states. Firstly, we show that any Tsallis relative $$\alpha $$?-entropies of coherence and $$l_{1}$$l1 norm of coherence give the same ordering for single-qubit pure states. However, they do not generate the same ordering for some high-dimensional states, even though these states are pure. Secondly, we also consider three special Tsallis relative $$\alpha $$?-entropies of coherence for $$\alpha =2, 1, \frac{1}{2}$$?=2,1,12 and show these three measures and $$l_{1}$$l1 norm of coherence will not generate the same ordering for some single-qubit mixed states. Nevertheless, they may generate the same ordering if we only consider a special subset of single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states. Finally, we discuss the degree of violation of between $$l_{1}$$l1 norm of coherence and Tsallis relative $$\alpha $$?-entropies of coherence. In a sense, this degree can measure the difference between these two coherence measures in ordering states.