Constructive method for detecting the information backflow of bijective non-completely-positive-divisible dynamics
Abstract
We investigate the relation between two approaches to the characterisation of quantum Markovianity, divisibility and lack of information backflow. We show that a bijective dynamical map is completely-positive-divisible if and only if a monotonic non-increase of distinguishability is observed for two equiprobable states of the evolving system and an ancilla. Moreover our proof is constructive: given any such map that is not completely-positive-divisible, we give an explicit construction of two states that, when taken with the same a priori probability, exhibit information back-flow. Finally, while an ancilla is necessary for the equivalence to hold in general, we show that it is always possible to witness the non-Markovianity of bijective maps without using any entanglement between system and ancilla.
Keywords
Cite
@article{arxiv.1603.04288,
title = {Constructive method for detecting the information backflow of bijective non-completely-positive-divisible dynamics},
author = {Bogna Bylicka and Markus Johansson and Antonio Acin},
journal= {arXiv preprint arXiv:1603.04288},
year = {2016}
}
Comments
Replaces arXiv:1603.04288v1. Error in proof of Lemma 1 for non-bijective dynamical maps in [v1]. Results unchanged for bijective dynamical maps. 7 pages, 1 figure