Infinite Dimensional Quantum Information Geometry
Mathematical Physics
2009-10-31 v1 Differential Geometry
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/0007039,
title = {Infinite Dimensional Quantum Information Geometry},
author = {M. R. Grasselli},
journal= {arXiv preprint arXiv:math-ph/0007039},
year = {2009}
}
Comments
Proceedings of the Disordered and Complex Systems, King's College, London, 10-14 July 2000 (satellite meeting of the ICMP2000)