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
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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
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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
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UT code for WoS article
000312832800018
EID of the result in the Scopus database
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