Notes on modified trace distance measure of coherence

Bin Chen and Shao-Ming Fei

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Submission date: 17. Jul. 2018
Pages: 13
published in: Quantum information processing, 17 (2018) 5, art-no. 107 
DOI number (of the published article): 10.1007/s11128-018-1879-9
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Abstract:
We investigate the modified trace distance measure of coherence recently introduced in [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 l₁-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 l₁-norm of coherence and the geometric measure of coherence.