Resource Preservability, Thermodynamics, and Classical Communication

Chung-Yun Hsieh^1*

¹Instituto de Ciencias Fotónicas (ICFO), Castelldefels, Barcelona, Spain

* Presenter:Chung-Yun Hsieh, email:andrew791006@gmail.com

Resource theory is a general 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. 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 a general class of resource preservability monotones based on channel distance measures. We apply our results to thermodynamics, showing that athermality preservability is related to the smallest bath size needed to thermalize all outputs of a Gibbs-preserving channel. As an application, unexpectedly, under a recently-studied thermalization model, we found that the smallest bath size needed to thermalize all outputs of a Gibbs-preserving coherence-annihilating channel upper bounds its one-shot classical capacity. In this sense, bath sizes can be interpreted as the thermodynamic cost of transmitting classical information. Our results give the first systematic and general formulation of the resource preservation character of free operations.

Keywords: Quantum Information Theory, Resource Theory, Quantum Thermodynamics, Classical Communication