Abstract

July 4 - 9.30-10.20
R. F. Streater - Dual structures on a quantum information manifold.

We find conditions on a manifold M of states of W*-algebra B(H) such that both the (+1) and the (-1) affine structures are defined on the tangent space. Sufficient conditions are that M consists of density operators D such that D^p is of trace class for all p>0, and that the topology is such that a neighbourhood of a point D(0) consists of all points D of M such that there exist c, C such that 0 < cD < D(0) < CD holds. An equivalent condition in terms of the Connes cocycle is derived. [an error occurred while processing this directive]