Resource Destroying Maps

TL;DR

This paper introduces a unified framework using resource destroying maps to analyze quantum resource theories, revealing fundamental connections and enabling simple, optimization-free resource measures for coherence and quantum correlations.

Contribution

It proposes a general scheme based on resource destroying maps, establishing conditions for resource-free operations and defining easily computable resource measures.

Findings

Resource destroying maps effectively characterize resource-free states and operations.

The framework applies to coherence and quantum correlations, providing new insights.

Simple resource measures that do not require optimization are introduced.

Abstract

Resource theory is a widely-applicable framework for analyzing the physical resources required for given tasks, such as computation, communication, and energy extraction. In this paper, we propose a general scheme for analyzing resource theories based on resource destroying maps, which leave resource-free states unchanged but erase the resource stored in all other states. We introduce a group of general conditions that determine whether a quantum operation exhibits typical resource-free properties in relation to a given resource destroying map. Our theory reveals fundamental connections among basic elements of resource theories, in particular, free states, free operations, and resource measures. In particular, we define a class of simple resource measures that can be calculated without optimization, and that are monotone nonincreasing under operations that commute with the resource destroying map. We apply our theory to the resources of coherence and quantum correlations (e.g., discord), two prominent features of nonclassicality.