Quantifying Operations with an Application to Coherence

TL;DR

This paper develops a framework to quantify the non-classicality of quantum operations, specifically coherence detection, using resource theories and resource destroying maps, with practical measures and evaluation methods.

Contribution

It introduces a novel resource-theoretic approach to quantify the coherence detection ability of quantum operations, including operational measures and evaluation techniques.

Findings

Two measures for coherence detection ability are proposed.

One measure has an operational interpretation.

Methods for evaluating these measures are provided.

Abstract

To describe certain facets of non-classicality, it is necessary to quantify properties of operations instead of states. This is the case if one wants to quantify how well an operation detects non-classicality, which is a necessary prerequisite for its use in quantum technologies. To do so rigorously, we build resource theories on the level of operations, exploiting the concept of resource destroying maps. We discuss the two basic ingredients of these resource theories, the free operations and the free super-operations, which are sequential and parallel concatenations with free operations. This leads to defining properties of functionals that are well suited to quantify the resources of operations. We introduce these concepts at the example of coherence. In particular, we present two measures quantifying the ability of an operation to detect, i.e. to use, coherence, one of them with an operational interpretation, and provide methods to evaluate them.