Ordering states with various coherence measures

Long-Mei Yang, Bin Chen, Shao-Ming Fei, and Zhi-Xi Wang

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Submission date: 17. Jul. 2018
Pages: 12
published in: Quantum information processing, 17 (2018) 4, art-no. 91 
DOI number (of the published article): 10.1007/s11128-018-1856-3
Bibtex
Keywords and phrases: $l_1$-norm of coherence, relative entropy of coherence, geometric measure of coherence, modified trace distance of coherence, ordering states
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Abstract:
Quantum coherence is one of the most significant theories in quantum physics. Ordering states with various coherence measures is an intriguing task in quantification theory of coherence. In this paper, we study this problem by use of four important coherence measures – the l₁ norm of coherence, the relative entropy of coherence, the geometric measure of coherence and the modified trace distance measure of coherence. We show that each pair of these measures give a different ordering of qudit states when d ≥ 3. However, for single-qubit states, the l₁ norm of coherence and the geometric coherence provide the same ordering. We also show that the relative entropy of coherence and the geometric coherence give a different ordering for single-qubit states. Then we partially answer the open question proposed in [Quantum Inf. Process. 15, 4189 (2016)] whether all the coherence measures give a different ordering of states.