Quantum statistical manifolds: the linear growth case

Abstract

A class of vector states on a von Neumann algebra is constructed. These states belong to a deformed exponential family. One specific deformation is considered. It makes the exponential function asymptotically linear. Difficulties arising due to non-commutativity are highlighted.Comment: 24 pages, 12pt, A4; improved version, now making use of the commutant algebr