International Journal of Theoretical Physics

, Volume 47, Issue 12, pp 3267–3272 | Cite as

Completely Entangled State and Simultaneous Eigenstate in a Finite Dimensional Space

  • Masashi Ban


It is shown that a completely entangled state belonging to a finite dimensional Hilbert space is equivalent to a simultaneous eigenstate of two unitary operators. These operators are exponentials of sum and difference of two Hermitian operators of a two-mode system that are complementary with each other.


Entangled state Simultaneous eigenstate Complementarity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Peres, A.: Quantum Theory: Concepts and Methods. Kluwer, New York (1993) MATHGoogle Scholar
  2. 2.
    Braunstein, S.L., Pati, A.K. (eds.): Quantum Information with Continuous Variables. Kluwer, Dordrecht (2003) MATHGoogle Scholar
  3. 3.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) MATHGoogle Scholar
  4. 4.
    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: LANL. quant-ph/0703044 (2003)
  5. 5.
    Santhanam, T.S., Tekumalla, A.R.: Found. Phys. 6, 583 (1976) CrossRefADSGoogle Scholar
  6. 6.
    Santhanam, T.S.: Found. Phys. 7, 121 (1977) CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Pegg, D.T., Barnett, S.M.: Phys. Rev. A 39, 1665 (1989) CrossRefADSGoogle Scholar
  8. 8.
    Barnett, S.M., Pegg, D.T.: Phys. Rev. A 41, 3427 (1990) CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Ban, M.: J. Phys. A 35, L193 (2002) MATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Fivel, D.I.: Phys. Rev. Lett. 74, 835 (1995) MATHCrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Pittenger, A.O., Rubin, M.H.: Phys. Rev. A 62, 32313 (2000) CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Graduate School of Humanities and SciencesOchanomizu UniversityBunkyo-kuJapan
  2. 2.CRESTJapan Science and Technology AgencyChuo-kuJapan

Personalised recommendations