Optimization free measures of quantum resources
arXiv:1711.10889 · doi:10.1103/PhysRevA.97.062344
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.
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
References in corpus (8)
- Measuring Quantum Coherence with Entanglement
- Reference frames, superselection rules, and quantum information
- The resource theory of quantum reference frames: manipulations and monotones
- Measuring the quality of a quantum reference frame: the relative entropy of frameness
- Quantifying the Imaginarity of Quantum Mechanics
- Translation of Lueders' "Uber die Zustandsanderung durch den Messprozess"
- A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
- Quantumness of correlations, quantumness of ensembles and quantum data hiding