Skip to main content
SpringerLink
Log in

Statistical Properties of Thermal State Under Quantum Hadamard Transform

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We study a new type of thermal state which is obtained by operating Hadamard operator on a thermal field. We call this new thermal state as quantum Hadamard’s thermal state (QHTS). The normally ordered form of QHTS is derived by using Weyl-ordering invariance under the similarity transformation and the Weyl correspondence scheme. We find that QHTS can be considered as squeezed state under certain conditions. The statistical properties of QHTS is also discussed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Kovalev, A.A., Dumer, I., Pryadko, L.P.: Phys. Rev. A 84, 062319 (2011)

    Article  ADS  Google Scholar 

  2. Meyer, D.A., Pommersheim, J.: Theor. Comput. Sci. 412, 7068–7074 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Nielsen, M.A., Chuang, I.L.: The Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  4. Preskill, J.: Quantum Information and Computation. California Institute of Technology (1998)

  5. Xu, X.L., Xu, S.M., Zhang, Y.H., Li, H.Q., Wang, J.S.: Chin. Phys. B 20, 010301 (2011)

    Article  ADS  Google Scholar 

  6. Seyfarth, U., Ranade, K.S.: Phys. Rev. A 84, 042327 (2011)

    Article  ADS  Google Scholar 

  7. Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 454, 339–354 (1998)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  8. Parker, S., Bose, S., Plenio, M.B.: Phys. Rev. A 61, 032305 (2000)

    Article  ADS  Google Scholar 

  9. Jiang, N.-Q., Zheng, Y.-Z.: Phys. Rev. A 74, 012306 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  10. Fan, H.-Y., Guo, Q.: Commun. Theor. Phys. 49, 859 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  11. Fan, H.-Y.: J. Opt. B, Quantum Semiclass. Opt. 5, R147 (2003)

    Article  ADS  Google Scholar 

  12. Fan, H.-Y.: Ann. Phys. 321, 480–494 (2006)

    Article  MATH  ADS  Google Scholar 

  13. Obada, A.S.F., Al-Kader, G.M.A.: J. Mod. Opt. 46, 263 (1999)

    ADS  Google Scholar 

  14. Jiang, N.-Q., Jin, B.-Q., Zhang, Y., Cai, G.-C.: Europhys. Lett. 84, 14002 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  15. Al-Kader, G.M.A.: J. Opt. B, Quantum Semiclass. Opt. 5, S228 (2003)

    Article  ADS  Google Scholar 

  16. Xu, X.-X., Yuan, H.-C., Hu, L.-Y., Fan, H.-Y.: J. Phys. A, Math. Theor. 44, 445306 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  17. Weyl, H.: The Classical Groups. Princeton University Press, Princeton (1953)

    Google Scholar 

  18. Zachos, C.: Int. J. Mod. Phys. A 17, 297 (2002)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  19. Xu, Y.J., Song, J., Yuan, H.C., Fan, H.Y., Liu, Q.Y.: Mod. Phys. Lett. A 26, 833 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Fan, H.-Y., Zaidi, H.R.: Phys. Lett. A 124, 303–307 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  21. Xu, X.X., Hu, L.Y., Fan, H.Y.: Mod. Phys. Lett. A 24, 2623–2630 (2009)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  22. Fan, H.Y.: Ann. Phys. 323, 500–526 (2008)

    Article  MATH  ADS  Google Scholar 

  23. Fan, H.Y., Fan, Y.: Int. J. Mod. Phys. A 17, 701–708 (2002)

    Article  MATH  ADS  Google Scholar 

  24. Glauber, R.J.: Phys. Rev. 130, 2529–2539 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  25. Glauber, R.J.: Phys. Rev. 131, 2766–2788 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  26. Puri, R.R.: Mathematical Methods of Quantum Optics. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

  27. Hong, C.K., Mandel, L.: Phys. Rev. A 32, 974–982 (1985)

    Article  ADS  Google Scholar 

  28. Lee, J., Kim, J., Nha, H.: J. Opt. Soc. Am. B 26, 1363–1369 (2009)

    Article  ADS  Google Scholar 

  29. Mandel, L.: Opt. Lett. 4, 205 (1979)

    Article  ADS  Google Scholar 

  30. Lambropoulos, P., Petrosyan, D.: Fundamentals of Quantum Optics and Quantum Information. Springer, Berlin (2007)

    Google Scholar 

  31. Ekert, A., Rzażewski, K.: Opt. Commun. 65, 225–228 (1988)

    Article  ADS  Google Scholar 

  32. Janszky, J., Yushin, Y.: Phys. Rev. A 36, 1288–1292 (1987)

    Article  ADS  Google Scholar 

  33. Wang, S., Fan, H.: J. Opt. Soc. Am. B 29, 15 (2012)

    Article  ADS  Google Scholar 

  34. Wigner, E.: Phys. Rev. 40, 749 (1932)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Huainan Normal University, Huainan, 232001, China

    Gang Ren & Jian-ming Du

Authors
  1. Gang Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian-ming Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gang Ren.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ren, G., Du, Jm. Statistical Properties of Thermal State Under Quantum Hadamard Transform. Int J Theor Phys 52, 779–787 (2013). https://doi.org/10.1007/s10773-012-1386-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-012-1386-1

Keywords

Search

Navigation