Skip to main content
SpringerLink
Log in

Quantum Erasure of Decoherence

  • Published:
Open Systems and Information Dynamics

Abstract

We consider the classical algebra of observables that are diagonal in a given orthonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one, while preserving the elements of the classical algebra. For quantum systems in dimension two and three any decoherence process can be undone by collecting classical information from the environment and using such an information to restore the initial system state. As a relevant example, we illustrate the quantum eraser of Scully et al. [Nature 351, 111 (1991)] as an example of environment-assisted correction, and present the generalization of the eraser setup for d-dimensional systems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Bibliography

  1. K. Kraus, States, Effects, and Operations: Fundamental Notions in Quantum Theory, Lect. Notes Phys. 190, Springer-Verlag, Berlin, 1983.

    Google Scholar 

  2. M. Gregoratti and R. F Werner, J. Mod. Opt. 50, 915 (2003).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. P. Hayden and C. King, Quantum Inform. Comput. 5, 156 (2005); J.A. Smolin, F. Verstraete, and A. Winter, Phys. Rev. A 72, 052317 (2005); A. Winter, quant-ph/0507045.

    MathSciNet  Google Scholar 

  4. M. Horodecki, J. Oppenheim, and A. Winter, Nature 436, 673 (2005); M. Horodecki, J. Oppenheim, and A. Winter, quant-ph/0512247.

    Article  ADS  Google Scholar 

  5. W.H. Zurek, Phys. Today 44, 36 (1991); W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003); M. Schlosshauer, Rev. Mod. Phys. 76, 1267 (2004).

    Google Scholar 

  6. P. Shor, Phys. Rev. A 52, 2493 (1995); A.M. Steane, Phys. Rev. Lett. 77, 793 (1996); P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1998); D. A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998); E. Knill et al., Phys. Rev. Lett. 84, 2525 (2000); A.Yu. Kitaev, Annals Phys. 303, 2 (2003); J. Preskill, in: Introduction to Quantum Computation, H.-K. Lo, S. Popescu, and T. Spiller. eds., World Scientic, Singapore, 1998.

    Article  ADS  Google Scholar 

  7. M.O. Scully and K. Drühl, Phys. Rev. A 25, 2208 (1982); M.O. Scully, B.-G. Englert, and H. Walther, Nature 351, 111 (1991); S. Dürr, T. Nonn, and G. Rempe, Nature 395, 33 (1998).

    ADS  Google Scholar 

  8. F. Buscemi, G. Chiribella, and G. M. D’Ariano, Phys. Rev. Lett. 95, 090501 (2005).

    Article  ADS  Google Scholar 

  9. M.-D. Choi, Lin. Alg. Appl. 10, 285 (1975).

    Article  MATH  Google Scholar 

  10. A. Jamiołkowski, Rep. Math. Phys. 3, 275 (1972).

    Article  Google Scholar 

  11. C.-K. Li and B.-S. Tam, SIAM J. Matrix Anal. Appl. 15, 903 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  12. W. F. Stinespring, Proc. Am. Math. Soc. 6, 211 (1955).

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Ozawa, J. Math. Phys. 25, 79 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  14. B. Schumacher, Phys. Rev. A 54, 2614 (1996).

    Article  ADS  Google Scholar 

  15. F. Buscemi, Phys. Lett. A 360, 256 (2006).

    Article  ADS  Google Scholar 

  16. M. O. Scully, B.-G. Englert, and H. Walther, Nature 351, 111 (1991).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Daini Hongo White Blgd. 201, 5–28–3 Hongo, Bunkyo-ku, 113-0033, Tokyo, Japan

    Francesco Buscemi

  2. Dip. di Fisica “A. Volta”, via Bassi 6, I-27100, Pavia, Italy

    Giulio Chiribella & Giacomo Mauro D’Ariano

Authors
  1. Francesco Buscemi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giulio Chiribella
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giacomo Mauro D’Ariano
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Francesco Buscemi.

Additional information

Presented at the 38th Symposium on Mathematical Physics “Quantum Entanglement & Geometry”, Toruń, June 4–7, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buscemi, F., Chiribella, G. & D’Ariano, G.M. Quantum Erasure of Decoherence. Open Syst Inf Dyn 14, 53–61 (2007). https://doi.org/10.1007/s11080-007-9028-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11080-007-9028-4

Keywords

Search

Navigation