Advertisement

Journal of Russian Laser Research

, Volume 39, Issue 4, pp 382–388 | Cite as

Sensitivity to Initial Noise in Measurement-Induced Nonlinear Quantum Dynamics

  • Orsolya Kálmán
  • Tamás Kiss
  • Igor Jex
Article
  • 19 Downloads

Abstract

We consider a special iterated quantum protocol with measurement-induced nonlinearity for qubits, where all pure initial states on the Bloch sphere can be considered chaotic. The dynamics is ergodic with no attractive fixed cycles. We show that initial noise radically changes this behavior. The completely mixed state is an attractive fixed point of the dynamics induced by the protocol. Our numerical simulations strongly indicate that initially mixed states all converge to the completely mixed state. The presented protocol is an example, where gaining information from measurements and employing it to control an ensemble of quantum systems enables us to create ergodicity which, in turn, is destroyed by any initial noise.

Keywords

post-selection measurement chaos nonlinear quantum transformation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Cvitanović, R. Artuso, R. Mainieri, et al., Chaos: Classical and Quantum, ChaosBook.org, Niels Bohr Institute, Copenhagen (2016).
  2. 2.
    H. Bechmann-Pasquinucci, B. Huttner, and N. Gisin, Phys. Lett. A, 242, 198 (1998).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A, 53, 2046 (1996).ADSCrossRefGoogle Scholar
  4. 4.
    C. H. Bennett, G. Brassard, S. Popescu, et al., Phys. Rev. Lett, 76, 722 (1996).ADSCrossRefGoogle Scholar
  5. 5.
    G. Alber, A. Delgado, N. Gisin, and I. Jex, J. Phys. A: Math. Gen., 34, 8821 (2001).ADSCrossRefGoogle Scholar
  6. 6.
    V. I. Man’ko and R. S. Puzko, J. Russ. Laser Res., 35, 362 (2014).CrossRefGoogle Scholar
  7. 7.
    V. I. Man’ko and R. S. Puzko, Eur. Phys. Lett., 109, 50005 (2015).ADSCrossRefGoogle Scholar
  8. 8.
    T. Kiss, I. Jex, G. Alber, and S. Vymětal, Phys. Rev. A, 74, 040301(R) (2006).ADSCrossRefGoogle Scholar
  9. 9.
    T. Kiss, S. Vymětal, L. D. Tóth, et al., Phys. Rev. Lett., 107, 100501 (2011).ADSCrossRefGoogle Scholar
  10. 10.
    A. Gilyen, T. Kiss, and I. Jex, Sci. Rep., 6, 20076 (2016).ADSCrossRefGoogle Scholar
  11. 11.
    J. W. Milnor, Dynamics in One Complex Variable, Princeton University Press (2006).Google Scholar
  12. 12.
    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010).Google Scholar
  13. 13.
    J. W. Milnor, Dynamics on the Riemann Sphere, Eur. Math. Soc., Zürich (2006).Google Scholar
  14. 14.
    S. Lloyd and J.-J. E. Slotine, Phys. Rev. A, 62, 012307 (2000).ADSCrossRefGoogle Scholar
  15. 15.
    J. M. Torres, J. Z. Bernád, G. Alber, et al., Phys. Rev. A, 95, 023828 (2017).ADSCrossRefGoogle Scholar
  16. 16.
    O. Kálmán and T. Kiss, Phys. Rev. A, 97, 032125 (2018).ADSCrossRefGoogle Scholar
  17. 17.
    In preparation.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Solid State Physics and Optics, Wigner Research Centre for PhysicsHungarian Academy of SciencesBudapestHungary
  2. 2.Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePraha 1 – Staré MěstoCzech Republic

Personalised recommendations