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Quantum resource theories

Eric Chitambar* and Gilad Gour†

Eric Chitambar*

  • Department of Electrical and Computer Engineering, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

Gilad Gour†

  • Department of Mathematics and Statistics, University of Calgary, Alberta, Canada T2N 1N4 and Institute for Quantum Science and Technology, University of Calgary, Alberta, Canada T2N 1N4

  • *echitamb@illinois.edu
  • †gour@ucalgary.ca
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Rev. Mod. Phys. 91, 025001 – Published 4 April, 2019

DOI: https://doi.org/10.1103/RevModPhys.91.025001

Abstract

Quantum resource theories (QRTs) offer a highly versatile and powerful framework for studying different phenomena in quantum physics. From quantum entanglement to quantum computation, resource theories can be used to quantify a desirable quantum effect, develop new protocols for its detection, and identify processes that optimize its use for a given application. Particularly, QRTs have revolutionized the way we think about familiar properties of physical systems such as entanglement, elevating them from being just interesting fundamental phenomena to being useful in performing practical tasks. The basic methodology of a general QRT involves partitioning all quantum states into two groups, one consisting of free states and the other consisting of resource states. Accompanying the set of free states is a collection of free quantum operations arising from natural restrictions placed on the physical system, restrictions that force the free operations to act invariantly on the set of free states. The QRT then studies what information processing tasks become possible using the restricted operations. Despite the large degree of freedom in how one defines the free states and free operations, unexpected similarities emerge among different QRTs in terms of resource measures and resource convertibility. As a result, objects that appear quite distinct on the surface, such as entanglement and quantum reference frames, appear to have great similarity on a deeper structural level. This article reviews the general framework of a quantum resource theory, focusing on common structural features, operational tasks, and resource measures. To illustrate these concepts, an overview is provided on some of the more commonly studied QRTs in the literature.

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Rev. Mod. Phys. 91, 025001– Published 4 April, 2019
  • Received 15 June 2018
Article part of CHORUS
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