Optimization free measures of quantum resources
Abstract
A closed expression is derived for the amount of resource present in a quantum state as quantified by a distance measure based on the \emph{Tsallis relative entropy} introduced recently in \cite{Zhao2018}, for any resource theory whose set of free states is described by the image of a unital \emph{resource destroying map}. By applying it to the resource theory of coherence it is demonstrated that the correct definition of a \emph{projective coarse grained measurement} needs to be modified in order for it to be correctly interpreted as a measurement which provides less information about a system's true state than the one obtained from a \emph{finer grained} measurement.
Cite
@article{arxiv.1711.10889,
title = {Optimization free measures of quantum resources},
author = {Nikolaos K. Kollas},
journal= {arXiv preprint arXiv:1711.10889},
year = {2018}
}
Comments
V1 incorrect due to existence of counterexample in the basic theorem in the case of a trace norm. V2 correct for a continuous set of new distance measures