Relative submajorization and its use in quantum resource theories
Abstract
We introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics, bipartite entanglement, and quantum coherence. In particular, we show that relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another, also when assisted by additional standard resources such as useful work or maximally-entangled states. These characterizations have a geometric formulation as the ratios or differences, respectively, between the Lorenz curves associated with the input and output resources. We also find several interesting bounds on the reversibility of a given transformation in terms of the properties of the forward transformation. The main technical tool used to establish these results is linear programming duality.
Cite
@article{arxiv.1510.03695,
title = {Relative submajorization and its use in quantum resource theories},
author = {Joseph M. Renes},
journal= {arXiv preprint arXiv:1510.03695},
year = {2016}
}
Comments
v2: fixed an error in the quantum coherence resource theory, added a constructive proof of relative majorization and comments on the relation to fluctuation theorems. v1: 35 pages, 6 figures. Comments very welcome!