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2010 | 8 | 6 | 1001-1014
Tytuł artykułu

Asymptotic evolution of random unitary operations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
6
Strony
1001-1014
Opis fizyczny
Daty
wydano
2010-12-01
online
2010-09-05
Twórcy
autor
  • Institut für Angewandte Physik, Technische Universität Darmstadt, Hochschulstraße 4a, D-64289, Darmstadt, Germany
autor
  • Department of Physics, FJFI ČVUT v Praze, Břehová 7 Praha 1 - Staré Město, 115 19, Prague, Czech Republic
Bibliografia
  • [1] S. Stenholm, K.-A. Suominen, Quantum Approach to Informatics (Wiley, New Jersey, 2005) http://dx.doi.org/10.1002/0471739367[Crossref]
  • [2] M. E. J. Newman, SIAM Rev. 45, 167 (2003) http://dx.doi.org/10.1137/S003614450342480[Crossref]
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  • [5] A. Lozinski, K. Życzkowski, W. Słomczyński, Phys. Rev. E 68, 046110 (2003) http://dx.doi.org/10.1103/PhysRevE.68.046110[Crossref]
  • [6] A. Baraviera, C. F. Lardizabal, A. O. Lopes, M. T. Cunha, arXiv:0911.0182v2 [WoS]
  • [7] J. Novotný, G. Alber, I. Jex, J. Phys. A-Math. Theor. 42, 282003 (2009) http://dx.doi.org/10.1088/1751-8113/42/28/282003[Crossref]
  • [8] A. S. Holevo, Statistical Structure of Quantum Theory (Springer, Berlin, 2001)
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  • [10] I. Bengtsson, K. Życzkowski, Geometry of Quantum States (Cambridge UP, Cambridge, 2006) http://dx.doi.org/10.1017/CBO9780511535048[Crossref]
  • [11] R. Bhatia, Positive Definite Matrices (Princeton UP, Princeton, 2007)
  • [12] W. Bruzda, V. Cappellini, H.-J. Sommers, K. Życzkowski, Phys. Lett. A 373, 320 (2009) http://dx.doi.org/10.1016/j.physleta.2008.11.043[Crossref]
  • [13] J. A. Holbrook, D. W. Kribs, R. Laflamme, Quantum Inf. Process 2, 381 (2004) http://dx.doi.org/10.1023/B:QINP.0000022737.53723.b4[Crossref]
  • [14] D. W. Kribs, P. Edinburgh Math. Soc. (Series 2) 46, 421 (2003) http://dx.doi.org/10.1017/S0013091501000980[Crossref]
  • [15] E. Knill, R. Laflamme, L. Viola, Phys. Rev. Lett. 84, 2525 (2000) http://dx.doi.org/10.1103/PhysRevLett.84.2525[Crossref]
  • [16] M. Hamermesh, Group Theory and Its Application to Physical problems (Dover Publications, New York, 1989)
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  • [18] G. Toth, J. J. G.-Ripoll, arXiv:quant-ph/0609052v3
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-010-0018-8
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