Abstract
We show that trace distance measure of coherence is a strong monotone for all qubit and, so called, states. An expression for the trace distance coherence for all pure states and a semidefinite program for arbitrary states is provided. We also explore the relation between -norm and relative entropy based measures of coherence, and give a sharp inequality connecting the two. In addition, it is shown that both -norm- and Schatten--norm–based measures violate the (strong) monotonicity for all .
- Received 10 November 2015
DOI:https://doi.org/10.1103/PhysRevA.93.012110
©2016 American Physical Society
Physics Subject Headings (PhySH)
Quantum Information, Science & TechnologyGeneral Physics