# Joint CAS-UIO seminar: Fred Shultz, Decomposing separable states

Fred Shultz, Wellesley College, USA will give a talk with title "Decomposing separable states".

This is the first in a joint seminar series organised by the Operator Algebra group (UiO), Several Complex Variable group (UiO) and the CAS group (http://www.cas.uio.no/research/1213functiontheory/index.php). The plan is to have seminars every other week.

Abstract: This talk will begin with a brief introduction to entanglement and its applications, since that motivates the mathematics to be discussed. In the title of this talk, a state is a positive linear functional on the tensor product of the algebras of m x m and n x n complex matrices. Such a state is separable if it is a convex combination of product states. An interesting open problem is to give a useful criterion for a state to be separable. A related problem is to give a systematic way to find a decomposition of a separable state into a convex combination of product states. This talk will describe such a decomposition for a class of separable states that is of both physical and mathematical interest. This decomposition is also applicable to a class of completely positive maps (which correspond to certain quantum channels). This is joint work with Erik Alfsen.