The exponential Orlicz space in quantum information geometry
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
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| _version_ | 1866909386917543936 |
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| author | Jenčová, Anna |
| author_facet | Jenčová, Anna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06906 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The exponential Orlicz space in quantum information geometry Jenčová, Anna Quantum Physics Mathematical Physics Operator Algebras 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. |
| title | The exponential Orlicz space in quantum information geometry |
| topic | Quantum Physics Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2301.06906 |