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Linear maps preserving maximal deviation and the Jordan structure of quantum systems

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F12%3A00198977" target="_blank" >RIV/68407700:21230/12:00198977 - isvavai.cz</a>

  • Result on the web

    <a href="http://link.aip.org/link/?JMP/53/122208" target="_blank" >http://link.aip.org/link/?JMP/53/122208</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1063/1.4771671" target="_blank" >10.1063/1.4771671</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Linear maps preserving maximal deviation and the Jordan structure of quantum systems

  • Original language description

    In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable isthe largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or aminus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only one numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviati

  • 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

    2012

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Journal of Mathematical Physics

  • ISSN

    0022-2488

  • e-ISSN

  • Volume of the periodical

    53

  • Issue of the periodical within the volume

    12

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    10

  • Pages from-to

  • UT code for WoS article

    000312832800018

  • EID of the result in the Scopus database