Ordering states with Tsallis relative α-entropies of coherence

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. Firstly, we show that any Tsallis relative a- entropies of coherence and 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 a- entropies of coherence for alpha= 2, 1, 1 2 and show these three measures and l1 norm of coherence will not generate the same ordering for some single-qubitmixed states. Nevertheless, they may generate the same ordering if we only consider a special subset of single-qubitmixed 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 l1 norm of coherence and Tsallis relative a- entropies of coherence. In a sense, this degree can measure the difference between these two coherence measures in ordering states.