Year: 2019
Type: article
Abstract: The resource theory of thermal operations aims at describing possible transitions of microscale systems interacting with a macroscale environment under the fundamental assumption of energy conservation. For initial quantum states diagonal in the basis of the local Hamiltonian, these transitions are completely described by thermal processes (TPs), which form a convex set. In this paper, we give a complete characterization of the set of states that can be achieved through TPs, by describing the boundary of the allowed set of states using the so-called thermomajorization curves as a tool. We address the problem of achieving a certain transition through a convex combination of products of extremal TPs. We characterize all extremal TPs by associating them with transportation matrices. It becomes evident that there are extremal TPs that are not required in the implementation of any transition allowed by TPs. The statement holds for every dimension $d\ensuremath{\ge}4$ of the state space. A property of the associated graphs, biplanarity, is identified as the distinguishing feature of these extremal TPs that are required for the arbitrary transition allowed by TPs.
Source: Physical Review A
Author: Paweł Mazurek
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Narodowe Centrum Nauki
Award: G94625023
OpenAlex ID: W2896083284