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MiS Preprint
53/2018

Ordering states with various coherence measures

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

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 $l_1$ 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 $d\geq 3$. However, for single-qubit states, the $l_1$ 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.

Received:
Jul 17, 2018
Published:
Jul 18, 2018
Keywords:
$l_1$-norm of coherence, relative entropy of coherence, geometric measure of coherence, modified trace distance of coherence, ordering states

Related publications

inJournal
2018 Repository Open Access
Long-Mei Yang, Bin Chen, Shao-Ming Fei and Zhi-Xi Wang

Ordering states with various coherence measures

In: Quantum information processing, 17 (2018) 4, p. 91