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Statements

Subject Item
n2:RIV%2F68407700%3A21340%2F12%3A00197439%21RIV13-MSM-21340___
rdf:type
n7:Vysledek skos:Concept
dcterms:description
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z(ni), i = 1, ... , k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces of dimensions n(1), ... , n(k). The symmetry group of the respective finite Heisenberg group is given by the quotient group of certain normalizer. This paper extends our previous investigation of bipartite quantum systems to arbitrary multipartite systems of the above type. It provides detailed description of the normalizers and the corresponding symmetry groups. The new class of symmetry groups represents a very specific generalization of symplectic groups over modular rings. As an application, a new proof of existence of the maximal set of mutually unbiased bases in Hilbert spaces of prime power dimensions is provided. A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z(ni), i = 1, ... , k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces of dimensions n(1), ... , n(k). The symmetry group of the respective finite Heisenberg group is given by the quotient group of certain normalizer. This paper extends our previous investigation of bipartite quantum systems to arbitrary multipartite systems of the above type. It provides detailed description of the normalizers and the corresponding symmetry groups. The new class of symmetry groups represents a very specific generalization of symplectic groups over modular rings. As an application, a new proof of existence of the maximal set of mutually unbiased bases in Hilbert spaces of prime power dimensions is provided.
dcterms:title
Symmetries of finite Heisenberg groups for multipartite systems Symmetries of finite Heisenberg groups for multipartite systems
skos:prefLabel
Symmetries of finite Heisenberg groups for multipartite systems Symmetries of finite Heisenberg groups for multipartite systems
skos:notation
RIV/68407700:21340/12:00197439!RIV13-MSM-21340___
n7:predkladatel
n14:orjk%3A21340
n3:aktivita
n20:P n20:Z
n3:aktivity
P(LC06002), P(LC505), Z(MSM6840770039)
n3:cisloPeriodika
28
n3:dodaniDat
n12:2013
n3:domaciTvurceVysledku
n21:2868059
n3:druhVysledku
n17:J
n3:duvernostUdaju
n4:S
n3:entitaPredkladatele
n11:predkladatel
n3:idSjednocenehoVysledku
172805
n3:idVysledku
RIV/68407700:21340/12:00197439
n3:jazykVysledku
n13:eng
n3:klicovaSlova
finite-dimensional quantum mechanics; composite systems; Heisenberg group; normalizer
n3:klicoveSlovo
n8:composite%20systems n8:Heisenberg%20group n8:normalizer n8:finite-dimensional%20quantum%20mechanics
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[DCA555B4A24B]
n3:nazevZdroje
Journal of Physics A: Mathematical and Theoretical
n3:obor
n19:BE
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n16:LC505 n16:LC06002
n3:rokUplatneniVysledku
n12:2012
n3:svazekPeriodika
45
n3:tvurceVysledku
Tolar, Jiří Korbelář, M.
n3:wos
000306117200011
n3:zamer
n9:MSM6840770039
s:issn
1751-8113
s:numberOfPages
18
n18:doi
10.1088/1751-8113/45/28/285305
n15:organizacniJednotka
21340