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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

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

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topologické a geometrické vlastnosti Banachových prostorů a operátorových algeber</a><br>

Návaznosti

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

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

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Svazek periodika

53

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

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Kód UT WoS článku

000312832800018

EID výsledku v databázi Scopus

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