Infinite Dimensional Quantum Information Manifolds

by M. R. Grasselli , in Disordered and Complex Systems (London 2000), ed: P. Sollich, A. C. C. Coolen, L. Hughston and R. F. Streater, Amer. Inst. of Phys. Conference Proceedings, Vol. 553, 141-146, 2001.


We present the construction of an infinite dimensional Banach manifold of quantum mechanical states on a Hilbert space H using different types of small perturbations of a given Hamiltonian. We provide the manifold with a flat connection, called the exponential connection, and comment on the possibility of introducing the dual mixture connection.

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