Resource Destroying Maps
Zi-Wen Liu, Xueyuan Hu, Seth Lloyd

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…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications
