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Currencies in Resource Theories

by 1 and 1,2,*
Institute for Theoretical Physcics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland
School of Physics, University of Bristol, Tyndall Avenue, Bristol BS8 1TH, UK
Author to whom correspondence should be addressed.
Academic Editors: Sebastian Deffner and Frederico Brito
Entropy 2021, 23(6), 755;
Received: 12 April 2021 / Revised: 9 June 2021 / Accepted: 11 June 2021 / Published: 15 June 2021
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of “currencies” to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out. Currencies are a subset of resources chosen to quantify all the other resources—like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions in the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work generalizes axiomatic approaches to thermodynamic entropy, work and currencies made of local copies. In particular, by applying our approach to the resource theory of unital maps, we derive operational single-shot entropies for arbitrary, non-probabilistic descriptions of resources. View Full-Text
Keywords: quantum resource theories; quantum thermodynamics; knowledge in physics quantum resource theories; quantum thermodynamics; knowledge in physics
MDPI and ACS Style

Kraemer, L.; del Rio, L. Currencies in Resource Theories. Entropy 2021, 23, 755.

AMA Style

Kraemer L, del Rio L. Currencies in Resource Theories. Entropy. 2021; 23(6):755.

Chicago/Turabian Style

Kraemer, Lea, and Lídia del Rio. 2021. "Currencies in Resource Theories" Entropy 23, no. 6: 755.

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