QUIGS SEMINAR: Eventually Entanglement Breaking Maps by Mizanur Rahaman

SPEAKER:  Mizanur Rahaman

Dept. of Pure Mathematics, University of Waterloo

ABSTRACT:

Since its introduction, the class of `entanglement breaking' maps
played a crucial role in the study of quantum information science and
also in the theory of completely positive maps. In this talk, I will
present a certain class of linear maps on matrix algebras that have
the property that they become entanglement breaking after compos-
ing nite or in nite number of times with themselves. These maps are
called `eventually entanglement breaking' maps. This means that the
Choi matrix of the iterated linear map becomes separable in the ten-
sor product space. It turns out that the set of eventually entanglement
breaking maps form a rich class within the set of all unital completely
positive maps. This analysis is motivated by the PPT-squared con-
jecture made by M. Christandl that says every PPT channel, when
composed with itself, becomes entanglement breaking. In this work, it
is proved that every unital PPT-channel becomes entanglement break-
ing after nite number of iterations. This is a joint work with Sam
Jaques and Vern Paulsen.