On complete positivity, Markovianity, and the quantum data-processing inequality, in the presence of initial system-environment correlations
Quantum Physics
2014-10-07 v3 Statistical Mechanics
Abstract
We show that complete positivity is not only sufficient but also necessary for the validity of the quantum data-processing inequality. As a consequence, the reduced dynamics of a quantum system are completely positive, even in the presence of initial correlations with its surrounding environment, if and only if such correlations do not allow any anomalous backward flow of information from the environment to the system. Our approach provides an intuitive information-theoretic framework to unify and extend a number of previous results.
Keywords
Cite
@article{arxiv.1307.0363,
title = {On complete positivity, Markovianity, and the quantum data-processing inequality, in the presence of initial system-environment correlations},
author = {Francesco Buscemi},
journal= {arXiv preprint arXiv:1307.0363},
year = {2014}
}
Comments
v3: to appear in Physical Review Letters, 5+3 pages, 2 color figures; v2: 10 pages, much improved, 2 figures; v1: 7 pages, preliminary version posted to encourage comments