The analytic quantum information manifold

Details The analytic quantum information manifold The analytic quantum information manifold

1999-10-22

arxiv.org/abs/math-ph/9910036v2

Physics

Mathematical Physics

12 pages LATEX; to appear in "Stochastic processes, physics and geometry: new interplays"; eds. F. Gesztesy, S. Paycha and H.

Scientific paper

Let H be a self-adjoint operator such that exp(-aH) is of trace class for
some a<1. Let V be a symmetric operator, Kato bounded relative to H. We show
that log Tr[exp(-H+xV)] is a real analytic function of x in a hood of x=0. We
show that the Gibbs states of H+xV form a real analytic Banach manifold. This
work has been extended in math-ph/9910031.

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