Skip to main content
Log in

Superposition Principle for Qubit States in the Spin-Projection Mean Representation

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We formulate the superposition principle of two states of qubit as a nonlinear addition rule of mean values of spin projections onto three perpendicular directions and obtain explicit expressions for the mean values determining the superposition states in terms of the mean values of two initial pure states of the qubit.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Schrödinger, Ann. Phys., 384, 361 (1926).

    Article  Google Scholar 

  2. E. Schrödinger, Ann. Phys., 384, 489 (1926).

    Article  Google Scholar 

  3. L. D. Landau, Z. Phys., 45, 430 (1927).

    Article  ADS  Google Scholar 

  4. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed., Oxford University Press (1982).

    Google Scholar 

  5. J. von Neumann, Gött. Nach., 1, 245 (1927).

  6. E. Wigner, Phys. Rev., 40, 749 (1932).

    Article  ADS  Google Scholar 

  7. K. Husimi, Proc. Phys. Math. Soc. Jpn., 22, 264 (1940).

    Google Scholar 

  8. R. J. Glauber, Phys. Rev. Lett., 131, 2766 (1963).

    ADS  MathSciNet  Google Scholar 

  9. E. C. G. Sudarshan, Phys. Rev. Lett., 10, 277 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  10. S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).

  11. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett., 70, 1244 (1993).

    Article  ADS  Google Scholar 

  12. R. L. Stratonovich, J. Exp. Theor. Phys., 4, 891 (1957).

    Google Scholar 

  13. P. Adam, V. A. Andreev, M. A. Man’ko, et al., J. Russ. Laser Res., 41, 470 (2020).

  14. S. Mancini, O. V. Man’ko, V. I. Man’ko, and P. Tombesi, J. Phys. A: Math. Gen., 34, 3461 (2001).

  15. V. I. Man’ko, G. Marmo, F. Ventriglia, and P. Vitale, J. Phys. A, 50, 335302 (2017).

  16. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 38, 141 (2017).

  17. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 38, 324 (2017).

  18. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 38, 416 (2017).

  19. W. K. Wootters, Found. Phys., 16, 391 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  20. V. V. Dodonov and V. I. Man’ko, Phys. Lett. A, 229, 335 (1997).

  21. V. I. Man’ko and O. V. Man’ko, J. Exp. Theor. Phys., 85, 430 (1997).

  22. M. A. Man’ko and V. I. Man’ko, Phys. Scr., 93, 084002 (2018).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrey Yu. Fedorov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fedorov, A.Y., Man’ko, V.I. Superposition Principle for Qubit States in the Spin-Projection Mean Representation. J Russ Laser Res 43, 82–89 (2022). https://doi.org/10.1007/s10946-022-10025-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-022-10025-6

Keywords

Navigation