Correlation between Correlations: Process and Time in Quantum Networks

  • Günter Mahler
  • Ilki Kim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1509)

Abstract

We study a special inhomogeneous quantum network consisting of a ring of M pseudo-spins (here M = 4) sequentially coupled to one and the same central spin under the influence of given pulse sequences (quantum gate operations). This architecture could be visualized as a quantum Turing machine with a cyclic “tape„. Rather than input-output-relations we investigate the resulting process, i.e. the correlation between one- and two-point expectation values (“correlations„) over various time-steps. The resulting spatiotemporal pattern exhibits many non-classical features including Zeno-effects, violation of temporal Bell-inequalities and quantum parallelism. Due to the strange web of correlations being built-up, specific measurement outcomes for the tape may refer to one or several preparation histories of the head. Specific families of correlation functions are more stable with respect to dissipation than the total wave-function.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ekert, A. and Jozsa, R.: Rev. Mod. Phys. 68 (1996) 1CrossRefMathSciNetGoogle Scholar
  2. 2.
    Barenco, A. et. al.: Phys. Rev. A 52 (1995) 3457CrossRefGoogle Scholar
  3. 3.
    Cirac, J. I. and Zoller, P.: Phys. Rev. Lett. 74 (1995) 4091CrossRefGoogle Scholar
  4. 4.
    Domokos, P., Raimond, J. M., Brune, M. and Haroche, S.: Phys. Rev. A 52 (1995) 3554CrossRefGoogle Scholar
  5. 5.
    Gershenfeld, N. A. and Chuang, I. L.: Science 275 (1997) 350CrossRefMathSciNetGoogle Scholar
  6. 6.
    Shnirman, A., Schön, G. and Hermon, Z.: Phys. Rev. Lett. 79 (1997) 2371CrossRefGoogle Scholar
  7. 7.
    Mahler, G. and Weberruss, V. A.: Quantum Networks: Dynamics of Open Nanostructures, Springer New York (1995); 2nd revised edition (1998)Google Scholar
  8. 8.
    Ferrero, M. and Santos, E.: Found. Phys. 27 (1997) 765CrossRefMathSciNetGoogle Scholar
  9. 9.
    Schlienz, J. and Mahler, G., Phys. Rev. A 52 (1995) 4396CrossRefGoogle Scholar
  10. 10.
    Deutsch, D.: Proc. Roy. Soc. A 400 (1985) 97MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Paz, J. P. and Mahler, G.: Phys. Rev. Lett. 71 (1993) 3235CrossRefGoogle Scholar
  12. 12.
    Obermayer, K., Teich, W. G. and Mahler, G.: Phys. Rev. B 37 (1988) 8111CrossRefGoogle Scholar
  13. 13.
    Misra, B. and Sudershan, E. C. G.: J. Math. Phys. 18 (1977) 756CrossRefGoogle Scholar
  14. 14.
    Knight, P.: Nature 344 (1990) 493CrossRefGoogle Scholar
  15. 15.
    Itano, W. M., Heinzen, D. J., Bollinger, J. J. and Wineland, D. J.: Phys. Rev. A 41 (1990) 2295CrossRefGoogle Scholar
  16. 16.
    Omnes, R.: Rev. Mod. Phys. 64 (1992) 339CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Günter Mahler
    • 1
  • Ilki Kim
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgartGermany

Personalised recommendations