Resource Preservability

TL;DR

This paper introduces a formal framework for quantifying how well free operations in resource theories preserve resources, providing new monotones and applications to thermodynamics and entanglement.

Contribution

It develops a systematic, axiomatic approach to measure resource preservability, including new monotones based on state and channel measures, with broad applications.

Findings

Resource preservability can be quantified using monotones derived from state and channel measures.

Athermality preservability relates to the minimal bath size for thermalization and bounds classical communication capacity.

New families of entanglement-preserving local thermalization processes are identified.

Abstract

Resource theory is a general, model-independent approach aiming to understand the qualitative notion of resource quantitatively. In a given resource theory, free operations are physical processes that do not create the resource and are considered zero-cost. This brings the following natural question: For a given free operation, what is its ability to preserve a resource? We axiomatically formulate this ability as the resource preservability, which is constructed as a channel resource theory induced by a state resource theory. We provide two general classes of resource preservability monotones: One is based on state resource monotones, and another is based on channel distance measures. Specifically, the latter gives the robustness monotone, which has been recently found to have an operational interpretation. As examples, we show that athermality preservability of a Gibbs-preserving channel can be related to the smallest bath size needed to thermalize all its outputs, and it also bounds the capacity of a classical communication scenario under certain thermodynamic constraints. We further apply our theory to the study of entanglement preserving local thermalization (EPLT) and provide a new family of EPLT which admits arbitrarily small nonzero entanglement preservability and free entanglement preservation at the same time. Our results give the first systematic and general formulation of the resource preservation character of free operations.