Transition probabilities of normal states determine the Jordan structure of a quantum system

DOI10.1063/1.4936404zbMath1330.81030arXiv1510.01487OpenAlexW2188110135MaRDI QIDQ2786617

No author found.

Publication date: 15 February 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.01487

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) General theory of von Neumann algebras (46L10) Applications of selfadjoint operator algebras to physics (46L60) States of selfadjoint operator algebras (46L30) Jordan structures on Banach spaces and algebras (17C65) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (5)

On extension of norm-additive maps between the positive unit spheres of \(\ell_q (\ell_p)\) ⋮ Maps preserving trace of products of matrices ⋮ The positive contractive part of a noncommutative \(L^{p}\)-space is a complete Jordan invariant ⋮ On a variant of Tingley's problem for some function spaces ⋮ Surjective \(L^2\)-isometries on the projection lattice

Cites Work

• Unnamed Item
• Unnamed Item
• The positive contractive part of a noncommutative \(L^{p}\)-space is a complete Jordan invariant
• Cônes autopolaires et algèbres de Jordan
• Pure state transformations induced by linear operators
• Selected preserver problems on algebraic structures of linear operators and on function spaces
• Comparison of Uhlmann's transition probability with the one induced by the natural positive cone of von Neumann algebras in standard form
• Pure states as a dual object for C*-algebras
• Complements to various Stone-Weierstrass theorems for \(C^*\)-algebras and a theorem of Shultz
• The transition probability in the state space of a \(^*\)-algebra
• On Bures distance and \(*\)-algebraic transition probability between inner derived positive linear forms over \(W^*\)-algebras
• Noncommutative \(L^p\) structure encodes exactly Jordan structure
• Measures on projections and physical states
• Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann
• Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem
• Generalization of Wigner's unitary-antiunitary theorem for indefinite inner product spaces
• Superposition, transition probabilities and primitive observables in infinite quantum systems
• Transition probability (fidelity) and its relatives
• Positive linear maps of operator algebras
• Isometries of operator algebras
• A generalized Schwarz inequality and algebraic invariants for operator algebras
• On the geometry of projections in certain operator algebras
• The standard form of von Neumann algebras.
• Mappings preserving zero products
• Transition probabilities of positive functionals on $*$-algebras
• On Partially Ordered Vector Spaces and Their Duals, with Applications to Simplexes and C*-Algebras
• An elementary proof for the non-bijective version of Wigner's theorem

This page was built for publication: Transition probabilities of normal states determine the Jordan structure of a quantum system