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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://link.aip.org/link/?JMP/53/122208
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 is the 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 a minus 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 deviation in the case of self-adjoint parts of von Neumann algebras proved by Molná 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 is the 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 a minus 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 deviation in the case of self-adjoint parts of von Neumann algebras proved by Molná (en)
Title	Linear maps preserving maximal deviation and the Jordan structure of quantum systems Linear maps preserving maximal deviation and the Jordan structure of quantum systems (en)
skos:prefLabel	Linear maps preserving maximal deviation and the Jordan structure of quantum systems Linear maps preserving maximal deviation and the Jordan structure of quantum systems (en)
skos:notation	RIV/68407700:21230/12:00198977!RIV13-GA0-21230___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP201/12/0290)
http://linked.open...iv/cisloPeriodika	12
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Hamhalter, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	147118
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/12:00198977
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	algebra; numerical analysis; quantum theory; statistical analysis (en)
http://linked.open.../riv/klicoveSlovo	algebra numerical analysis statistical analysis quantum theory
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[48BD3E6B2F5D]
http://linked.open...i/riv/nazevZdroje	Journal of Mathematical Physics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Topological and geometrical properties of Banach spaces and operator algebras
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	53
http://linked.open...iv/tvurceVysledku	Hamhalter, Jan
http://linked.open...ain/vavai/riv/wos	000312832800018
issn	0022-2488
number of pages	10 (xsd:int)
http://bibframe.org/vocab/doi	10.1063/1.4771671
http://localhost/t...ganizacniJednotka	21230

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