Nothing Special   »   [go: up one dir, main page]

Skip to main content

Computation in Sofic Quantum Dynamical Systems

  • Conference paper
Unconventional Computation (UC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4618))

Included in the following conference series:

Abstract

We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information storage and processing in terms of entropy rate and excess entropy, giving closed-form expressions where possible. To illustrate the impact of measurement on information storage in quantum processes, we analyze two spin-1 sofic quantum systems that differ only in how they are measured.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Kitchens, B.P.: Symbolic dynamics: one-sides, two-sided, and countable state Markov shifts. Springer, Heidelberg (1998)

    Google Scholar 

  2. Hedlund, G.H., Morse, M.: Symbolic dynamics i. Amer. J. Math. 60, 815–866 (1938)

    Article  MathSciNet  Google Scholar 

  3. Hedlund, G.H., Morse, M.: Symbolic dynamics ii. Amer. J. Math. 62, 1–42 (1940)

    Article  MathSciNet  Google Scholar 

  4. Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press, Champaign-Urbana (1962)

    Google Scholar 

  5. Lind, D., Marcus, B.: An introduction to symbolic dynamics and coding. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  6. Gutzwiller, M.C.: Chaos in Classical and Quantum Mechanics. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  7. Reichl, L.E.: The transition to chaos: Conservative classical systems and quantum manifestations. Springer, New York (2004)

    MATH  Google Scholar 

  8. Habib, S., Jacobs, K., Shizume, K.: Emergence of chaos in quantum systems far from the classical limit. Phys. Rev. Lett. 96, 10403–10406 (2006)

    Article  Google Scholar 

  9. Alicki, R., Fannes, M.: Quantum dynamical systems. Oxford University Press, Oxford (2001)

    MATH  Google Scholar 

  10. Beck, C., Graudenz, D.: Symbolic dynamics of successive quantum-mechanical measurements. Phys. Rev. A 46(10), 6265–6276 (1992)

    Article  MathSciNet  Google Scholar 

  11. Wiesner, K., Crutchfield, J.P.: Computation in finitary quantum processes. e-print arxiv/quant-ph/0608206, 2006 (submitted)

    Google Scholar 

  12. Cover, T., Thomas, J.: Elements of Information Theory. Wiley-Interscience, Chichester (1991)

    MATH  Google Scholar 

  13. Albert, D.Z.: On quantum-mechanical automata. Physics Letters 98A, 249–251 (1983)

    Google Scholar 

  14. Peres, A.: On quantum-mechanical automata. Physics Letters 101A, 249–250 (1984)

    MathSciNet  Google Scholar 

  15. Moore, C., Crutchfield, J.P.: Quantum automata and quantum grammars. Theor. Comp. Sci. 237, 275–306 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: 38th IEEE Conference on Foundations of Computer Science, pp. 66–75. IEEE Computer Society Press, Los Alamitos (1997)

    Google Scholar 

  17. Aharonov, D., Kitaev, A., Nisan, N.: Quantum circiuts with mixed states. In: 30th Annual ACM Symposium on the Theory of Computing, pp. 20–30. ACM Press, New York (1998)

    Google Scholar 

  18. Ambainis, A., Watrous, J.: Two-way finite automata with quantum and classical states. Theoretical Computer Science 287, 299–311 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Freivalds, R., Winter, A.: Quantum finite state transducers. Lect. Notes Comp. Sci. vol. 2234, pp. 233–242 (2001)

    Google Scholar 

  20. Peres, A.: Quantum theory: concepts and methods. Kluwer Academic Publishers, Dordrecht (1993)

    MATH  Google Scholar 

  21. Hirsch, M., Palis, J., Pugh, C., Shu, M.: Neighborhoods of hyperbolic sets. Inventiones Math. 9, 121–134 (1970)

    Article  MATH  Google Scholar 

  22. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (2001)

    MATH  Google Scholar 

  23. Bishop, C.M.: Pattern recognition and machine learning. Springer Verlag, Singapore (2006)

    MATH  Google Scholar 

  24. Weiss, B.: Subshifts of finite type and sofic systems. Monatshefte für Mathematik 77, 462–474 (1973)

    Article  MATH  Google Scholar 

  25. Crutchfield, J.P., Feldman, D.P.: Regularities unseen, randomness observed: Levels of entropy convergence. Chaos 13, 25–54 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  26. Crutchfield, J.P., Wiesner, K.: Intrinsic quantum computation. , e-print arxiv/quant-ph/0611202, 2006 (submitted)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Selim G. Akl Cristian S. Calude Michael J. Dinneen Grzegorz Rozenberg H. Todd Wareham

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wiesner, K., Crutchfield, J.P. (2007). Computation in Sofic Quantum Dynamical Systems. In: Akl, S.G., Calude, C.S., Dinneen, M.J., Rozenberg, G., Wareham, H.T. (eds) Unconventional Computation. UC 2007. Lecture Notes in Computer Science, vol 4618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73554-0_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73554-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73553-3

  • Online ISBN: 978-3-540-73554-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics