Eventually Entanglement Breaking Maps
Abstract
We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor product space. If a linear map is entanglement breaking after finite iterations, we say the map has a finite index of separability. In particular we show that every unital PPT-channel becomes entanglement breaking after a finite number of iterations. It turns out that the class of unital channels that have finite index of separability is a dense subset of the unital channels. We construct concrete examples of maps which are not PPT but have finite index of separability. We prove that there is a large class of unital channels that are asymptotically entanglement breaking. This analysis is motivated by the PPT-squared conjecture made by M. Christandl that says every PPT channel, when composed with itself, becomes entanglement breaking.
Keywords
Cite
@article{arxiv.1801.05542,
title = {Eventually Entanglement Breaking Maps},
author = {Mizanur Rahaman and Samuel Jaques and Vern I. Paulsen},
journal= {arXiv preprint arXiv:1801.05542},
year = {2018}
}
Comments
A simple proof of Theorem 5.2, suggested by the referee, has been added. Some references are updated