MACNAUGHTON BLDG ROOM 434

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.