A construction of a nonparametric quantum information manifold

摘要

We present a construction of a Banach manifold structure on the set of faithful normal states of a von Neumann algebra, where the underlying Banach space is a quantum analogue of an Orlicz space. On the manifold, we introduce the exponential and mixture connections as dual pair of affine connections. (C) 2006 Elsevier Inc. All rights reserved.