Bures distance function and a generalization o f Sakai's non-commutative Radon-Nikodym theorem

DOI10.2977/prims/1195193113zbMath0252.46075OpenAlexW2070521974MaRDI QIDQ2557434

Huzihiro Araki

Publication date: 1972

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195193113

Mathematics Subject Classification ID

Representations of topological algebras with involution (46K10) General theory of von Neumann algebras (46L10)

Related Items (16)

Density operators as an arena for differential geometry ⋮ Geometric phases and related structures ⋮ A Radon-Nikodym type theorem for forms ⋮ Statistical inference in non-commutative probability ⋮ Two states ⋮ BURES DISTANCE FOR COMPLETELY POSITIVE MAPS ⋮ Structure theorem of the generator of a norm continuous completely positive semigroup: an alternative proof using Bures distance ⋮ Spheres and hemispheres as quantum state spaces ⋮ A continuity theorem for Stinespring's dilation ⋮ One-parameter family of Radon-Nikodym theorems for states of a von Neumann algebra ⋮ Bures distance and relative entropy ⋮ On a connection governing parallel transport along \(2 \times{}2\) density matrices ⋮ A remark on an infinite tensor product of von Neumann algebras ⋮ Limits of states ⋮ A remark on transition probability ⋮ Some properties of the Riemannian Bures metric on mixed states

Cites Work

• Tomita's theory of modular Hilbert algebras and its applications
• A non-commutative extension of abstract integration

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