Speaker: Mizanur Rahaman (University of Waterloo, Waterloo, Canada)
Date: 10 July 2018
Time: 3 pm
Venue: LH-1, Mathematics Department
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 composing
finite or infinite 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 tensor
product space. It turns out that the set of eventually entanglement
breaking maps forms a rich class within the set of all unital completely
positive maps. I will relate these maps with irreducible positive linear
maps which have been studied a lot in the non-commutative Perron-Frobenius theory.
Various spectral properties of a ucp map on finite dimensional C*-algebras will be discussed.
The motivation of this work is the “PPT-squared conjecture”
made by M. Christandl that says that every PPT channel, when
composed with itself, becomes entanglement breaking. In this work, it
is proved that every unital PPT-channel becomes entanglement breaking
after finite number of iterations.
This is a joint work with Sam
Jaques and Vern Paulsen.