The general structure of quantum resource theories

TL;DR

This paper explores the fundamental structure of quantum resource theories, showing that under certain conditions, they are asymptotically reversible with a unique resource measure linked to relative entropy.

Contribution

It provides a general framework for understanding the asymptotic reversibility of quantum resource theories and identifies the regularized relative entropy as the key resource measure.

Findings

QRTs are asymptotically reversible under maximal allowed operations.

The asymptotic conversion rate is given by the regularized relative entropy of the resource.

The resource measure equals the smoothed logarithmic robustness in the asymptotic limit.

Abstract

In recent years it was recognized that properties of physical systems such as entanglement, athermality, and asymmetry, can be viewed as resources for important tasks in quantum information, thermodynamics, and other areas of physics. This recognition followed by the development of specific quantum resource theories (QRTs), such as entanglement theory, determining how quantum states that cannot be prepared under certain restrictions may be manipulated and used to circumvent the restrictions. Here we discuss the general structure of QRTs, and show that under a few assumptions (such as convexity of the set of free states), a QRT is asymptotically reversible if its set of allowed operations is maximal; that is, if the allowed operations are the set of all operations that do not generate (asymptotically) a resource. In this case, the asymptotic conversion rate is given in terms of the regularized relative entropy of a resource which is the unique measure/quantifier of the resource in the asymptotic limit of many copies of the state. This measure also equals the smoothed version of the logarithmic robustness of the resource.