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Some Quantum Gate Operators for Continuum Variables in q-Deformed Coordinate Representation

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Abstract

By virtue of deformation quantization methods we introduce the q-deformed coordinate representation. A new set of completeness and orthogonality relations composed of the ket and bra which are not mutually Hermitian conjugates are derived. Further, using the eigenket and eigenbra for q-deformed coordinate some important quantum gate operators for continuum variables are realized and their properties are discussed.

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References

  1. Bennett, C.H.: Phys. Today 48, 24 (1995)

    Article  Google Scholar 

  2. Shor, P.W.: Phys. Rev. A 52, R2493 (1995)

    Article  ADS  Google Scholar 

  3. Ekert, A., Jozsa, R.: Rev. Mod. Phys. 68, 733 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  4. He, Y., Jiang, N.Q.: Opt. Commun. 283, 1558 (2010)

    Article  ADS  Google Scholar 

  5. He, Y., Jiang, N.Q., Ji, Y.Y.: Opt. Commun. 283, 1979 (2010)

    Article  ADS  Google Scholar 

  6. Eckert, A., Macchiavello, C.: An overview of quantum computing. In: Macchiavello, C., Palma, G.M., Zeilinger, A. (eds.) Quantum Computation and Quantum Information Theory. World Scientific, Singapore (2000)

    Google Scholar 

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

    Google Scholar 

  8. Gangopadhyay, D.: Int. J. Quantum Inf. 6, 471 (2008)

    Article  MATH  Google Scholar 

  9. Arik, M., Coon, D.D.: J. Math. Phys. 17, 4 (1976)

    Article  MathSciNet  Google Scholar 

  10. Macfarlane, A.: J. Phys. A, Math. Gen. 22, 4581 (1989)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Gray, R.W., Nelson, C.A.: J. Phys. A, Math. Gen. 23, L945 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  12. Chaturvedi, S., Srinivasan, V.: Phys. Rev. A 44, 8020 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  13. Man’ko, V.I., Marmo, G., Sudarshan, E.C.G., Zaccaria, F.: Phys. Scr. 55, 528 (1997)

    Article  ADS  Google Scholar 

  14. Biedenharn, L.C.: J. Phys. A 22, L873 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  15. Chaichian, M., Ellinas, D., Kulish, P.: Phys. Rev. Lett. 65, 980 (1990)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. Jurco, B.: Lett. Math. Phys. 21, 51 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. Kulish, P.P., Damaskinsky, E.V.: J. Phys. A 23, L415 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  18. Brachen, A.J., et al.: J. Phys. A 24, 1379 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  19. Meng, X.G., Wang, J.S., Li, H.Q.: Chin. Phys. B 17, 2973 (2008)

    Article  ADS  Google Scholar 

  20. Meng, X.G., Wang, J.S.: Int. J. Theor. Phys. 46, 1307 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  21. Song, T.Q., Fan, H.Y.: Int. J. Theor. Phys. 41, 695 (2007)

    Article  MathSciNet  Google Scholar 

  22. Fan, H.Y., Jing, S.C.: Phys. Lett. A 179, 379 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  23. Fan, H.Y., Zaidi, H.R., Klauder, J.R.: Phys. Rev. D 35, 1831 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  24. Fan, H.Y., Klauder, J.R.: Phys. Rev. A 49, 704 (1994)

    Article  ADS  MATH  Google Scholar 

  25. Fan, H.Y., Fan, Y.: Phys. Rev. A 54, 958 (1996)

    Article  Google Scholar 

  26. Fan, H.Y., Jiang, N.Q.: Mod. Phys. Lett. A 24, 1219 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  27. Jiang, N.Q., Jin, B.Q., Zang, Y., Cai, G.C.: Europhys. Lett. 84, 14002 (2008)

    Article  ADS  Google Scholar 

  28. Jiang, N.Q., Zang, Y.Z.: Phys. Rev. A 74, 012306 (2006)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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Correspondence to Ye-jun Xu.

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Xu, Yj., Song, J., Fan, Hy. et al. Some Quantum Gate Operators for Continuum Variables in q-Deformed Coordinate Representation. Int J Theor Phys 50, 744–751 (2011). https://doi.org/10.1007/s10773-010-0610-0

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  • DOI: https://doi.org/10.1007/s10773-010-0610-0

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