# Fred Shultz, Wellesley College (USA)

Fred Shultz, Wellesley College (USA) will give a talk with title "Affine automorphisms of the convex set of separable states, and decompositions of separable states".

Abstract: A state on the tensor product of m x m and n x n matrices

is separable if it can be written as a convex combination of pure

product states. These are precisely the states that are not

entangled. The set S of all separable states is compact and convex.

Given such a state there may be more than one decomposition into pure

product states. This is related to the facial structure of S. In

general faces of S are a combination of faces like those in the usual

state space, together with faces that are simplicial in nature.

Uniqueness of decompositions is related to simplicial structure.

Given any convex set, one wants to know its affine automorphisms.

These also are important in physical applications, since time

evolution of state spaces is represented by a one parameter family of

affine automorphisms. We give a description of all affine

automorphisms of the space S of separable states, and describe their

relationship to time evolution of the set of all states that preserves

separability and entanglement.