Ordering states with various coherence measures

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


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 \(d\ge 3\). 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 Liu et al. (Quantum Inf Process 15:4189, 2016) whether all the coherence measures give a different ordering of states.


\(l_1\) norm of coherence Relative entropy of coherence Geometric measure of coherence Modified trace distance of coherence Ordering states 



This work is supported by the NSFC under Number 11675113.


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Authors and Affiliations

  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  2. 2.School of Mathematical SciencesTianjin Normal UniversityTianjinChina

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