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arXiv · 2301.06906

The exponential Orlicz space in quantum information geometry

Anna Jenčová
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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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Anna Jenčová. 2023-01-13. The exponential Orlicz space in quantum information geometry. https://doi.org/10.1007/s41884-023-00097-x

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