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Orthogonal Measures on State Spaces and Context Structure of Quantum Theory

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00300844" target="_blank" >RIV/68407700:21230/16:00300844 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1007/s10773-016-2964-4" target="_blank" >http://dx.doi.org/10.1007/s10773-016-2964-4</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s10773-016-2964-4" target="_blank" >10.1007/s10773-016-2964-4</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Orthogonal Measures on State Spaces and Context Structure of Quantum Theory

  • Original language description

    An interplay between recent topos theoretic approach and standard convex theoretic approach to quantum theory is discovered. Combining new results on isomorphisms of posets of all abelian subalgebras of von Neumann algebras with classical Tomita's theorem from state space Choquet theory, we show that order isomorphisms between the sets of orthogonal measures (resp. finitely supported orthogonal measures) on state spaces endowed with the Choquet order are given by Jordan au-isomorphims between corresponding operator algebras. It provides new complete Jordan invariants for sigma-finite von Neumann algebras in terms of decompositions of states and shows that one can recover physical system from associated structure of convex decompositions (discrete or continuous) of a fixed state.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2016

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    International Journal of Theoretical Physics

  • ISSN

    0020-7748

  • e-ISSN

  • Volume of the periodical

    55

  • Issue of the periodical within the volume

    7

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    13

  • Pages from-to

    3353-3365

  • UT code for WoS article

    000378746600027

  • EID of the result in the Scopus database