Notes on modified trace distance measure of coherence

  • Bin Chen
  • Shao-Ming Fei


We investigate the modified trace distance measure of coherence recently introduced in Yu et al. [Phys. Rev. A 94, 060302(R), 2016]. We show that for any single-qubit state, the modified trace norm of coherence is equal to the \(l_{1}\)-norm of coherence. For any d-dimensional quantum system, an analytical formula of this measure for a class of maximally coherent mixed states is provided. The trade-off relation between the coherence quantified by the new measure and the mixedness quantified by the trace norm is also discussed. Furthermore, we explore the relation between the modified trace distance measure of coherence and other measures such as the \(l_{1}\)-norm of coherence and the geometric measure of coherence.


Modified trace distance of coherence Trace norm of coherence Maximally coherent Mixed states 



This work is supported by the NSF of China under Grant No. 11675113.


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Authors and Affiliations

  1. 1.School of Mathematical SciencesTianjin Normal UniversityTianjinChina
  2. 2.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  3. 3.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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