About: Asymptotic Evolution of Random Unitary Operations

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Description	We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits. We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits. (en)
Title	Asymptotic Evolution of Random Unitary Operations Asymptotic Evolution of Random Unitary Operations (en)
skos:prefLabel	Asymptotic Evolution of Random Unitary Operations Asymptotic Evolution of Random Unitary Operations (en)
skos:notation	RIV/68407700:21340/10:00171883!RIV11-MSM-21340___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC06002), Z(MSM6840770039)
http://linked.open...iv/cisloPeriodika	6
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Novotný, Jaroslav Jex, Igor
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 jaderná a fyzikálně inženýrská
http://linked.open...dnocenehoVysledku	248001
http://linked.open...ai/riv/idVysledku	RIV/68407700:21340/10:00171883
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	random unitary map; asymptotic evolution; iterations; attractor; open dynamics (en)
http://linked.open.../riv/klicoveSlovo	attractor asymptotic evolution iterations open dynamics random unitary map
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[53836A3DDB96]
http://linked.open...i/riv/nazevZdroje	Central European Journal of Physics
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Doppler Institute for Mathematical Physics and Applied Mathematics
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	8
http://linked.open...iv/tvurceVysledku	Alber, G. Jex, Igor Novotný, Jaroslav
http://linked.open...ain/vavai/riv/wos	000282330000019
http://linked.open...n/vavai/riv/zamer	Matematické, počítačové a experimentální metody ve fyzice
issn	1895-1082
number of pages	14 (xsd:int)
http://localhost/t...ganizacniJednotka	21340
is http://linked.open...avai/riv/vysledek of	Asymptotic Evolution of Random Unitary Operations Asymptotic Evolution of Random Unitary Operations Asymptotic Evolution of Random Unitary Operations

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