Quantum resource theories

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 like 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.

Optimal common resource in majorization-based resource theories

“…To see that, take two consecutive indices, k k , A.2. Proof of lemma 1 We prove now that x v vert inf inf…”

Channel activation of CHSH nonlocality

“…States of a qubit system can be expressed as 3 is called the Bloch vector of the state and s s s s = , ,…”

“…The most celebrated method for revealing the nonlocal features of quantum theory was proposed by John Bell in 1964, in what is now known as violating a Bell Inequality [1,2]. In recent years, nonlocality has been identified as a resource in quantum information theory [3], with applications in quantum cryptography [4,5], quantum key distribution [6] and quantum randomness [7].…”

“…These previous works only considered activation of nonlocality on the level of quantum states. This analysis can be understood from a resource-theoretic perspective in which nonlocality is regarded as a static quantum resource, manifesting in different multipartite quantum states in different extents [3]. Activation then describes a particular way of harnessing this resource among two or more quantum states.…”

Distributed Encoding and Decoding of Quantum Information over Networks

“…This paper aims to quantitatively characterize nonlocal properties of transformations for encoding and decoding in the distributed settings, adopting a resource theoretical approach. Resource theories aim to provide a quantitative understanding and an operational meaning of abstract physical attributes, such as entanglement in quantum mechanics and entropy in classical thermodynamics . In the theory of entanglement, a class of operations, such as local operations and classical communication (LOCC), is adopted as free operations, to which available operations for achieving a given task are restricted.…”