Optimization free measures of quantum resources

TL;DR

This paper derives a closed-form expression for quantum resource quantification using Tsallis relative entropy, applicable to resource theories with unital resource destroying maps, and clarifies the interpretation of projective coarse grained measurements.

Contribution

It provides a new analytical formula for quantum resource measures based on Tsallis entropy for a broad class of resource theories.

Findings

Derived a closed expression for resource quantification.

Applied the formula to the resource theory of coherence.

Revised the interpretation of projective coarse grained measurements.

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.