The exponential Orlicz space in quantum information geometry
- URL: http://arxiv.org/abs/2301.06906v1
- Date: Fri, 13 Jan 2023 09:38:34 GMT
- Title: The exponential Orlicz space in quantum information geometry
- Authors: Anna Jen\v{c}ov\'a
- Abstract summary: We construct a quantum version of the exponential Orlicz space.
We show that the constructed manifold admits a canonical divergence satisfying a Pythagorean relation.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We review the construction of a quantum version of the exponential
statistical manifold over the set of all faithful normal positive functionals
on a von Neumann algebra. The construction is based on the relative entropy
approach to state perturbation. We construct a quantum version of the
exponential Orlicz space and discuss the properties of this space and its dual
with respect to Kosaki $L_p$-spaces. We show that the constructed manifold
admits a canonical divergence satisfying a Pythagorean relation. We also prove
that the manifold structure is invariant under sufficient channels.
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