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.

24 pages, 12pt, A4; improved version, now making use of the commutant algebra

References in corpus (2)

• Quantum Statistical Manifolds
• Log-affine geodesics in the manifold of vector states on a von Neumann algebra

Cited by in corpus (3)

• Quantum Statistical Manifolds
• Log-affine geodesics in the manifold of vector states on a von Neumann algebra
• A Class of Non-Parametric Statistical Manifolds modelled on Sobolev Space