Schmidt-Mode Analysis of Entanglement for Quantum Information Studies

  • J. H. Eberly
  • K. W. Chan
  • C. K. Law
Conference paper
Part of the NATO Science Series book series (NAII, volume 113)


We present examples of the analysis of quantum entanglement entanglement as an introduction to the fundamental basis for quantum computing and information technology. Pure non-separable two-particle states are analysed using the Schmidt decomposition and we introduce the number of effective eigenmodes as a measure of entanglement. We give an elementary illustration, as well as an overview of more complex calculations we have carried out in situations involving bipartite states in continuous Hilbert space.


Spontaneous Emission Quantum Communication Rydberg Atom Double Ionization Bipartite State 
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  1. [1]
    For a review of quantum information devices, see H. E. Brandt, Prog. Quantum Electron. 22, 257 (1998), and references therein.ADSCrossRefGoogle Scholar
  2. [2]
    C. P. Williams and S. H. Clearwater, Explorations in Quantum Computing (TELOS, Santa Clara, 1998); and also Ultimate Zero and One: Computing at the Quantum Frontier (Copernicus, New York, 2000).Google Scholar
  3. [3]
    M. A. Nielson and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, New York, 2000).Google Scholar
  4. [4]
    C. K. Hong and L. Mandel, Phys. Rev. Lett. 56, 58 (1986), see also a similar idea in C. Adlard, E. R. Pike and S. Sarkar, Phys. Rev. lett. 79, 1585 (1997).ADSCrossRefGoogle Scholar
  5. [5]
    H. Huang and J. H. Eberly, J. Mod. Opt. 40, 915 (1993).ADSCrossRefGoogle Scholar
  6. [6]
    C. K. Law, I. A. Walmsley and J. H. Eberly, Phys. Rev. Lett. 84, 5304 (2000).ADSCrossRefGoogle Scholar
  7. [7]
    H. H. Arnaut and G. Barbosa, Phys. Rev. Lett. 85, 286 (2000).ADSCrossRefGoogle Scholar
  8. [8]
    See other Lectures in this Institute by L. A. Lugiato and A. Gatti.Google Scholar
  9. [9]
    A. Ekert and P. L. Knight, Am. J. Phys. 63, 415 (1995), and see references therein.MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. [10]
    L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).Google Scholar
  11. [11]
    S. Parker, S. Bose and M. B. Plenio, Phys. Rev. A 61, 032305 (2000).ADSCrossRefGoogle Scholar
  12. [12]
    R. Grobe, K. Rzązewski and J. H. Eberly, J. Phys. B 27, L503 (1994).ADSCrossRefGoogle Scholar
  13. [13]
    W.-C. Liu and J. H. Eberly, Phys. Rev. Lett. 83, 523 (1999).ADSGoogle Scholar
  14. [14]
    K. W. Chan, C. K. Law and J. H. Eberly, Phys. Rev. Lett. 88, 100402 (2002).ADSCrossRefGoogle Scholar
  15. [15]
    C. Kurtsiefer, et al., Phys. Rev. A 55, R2539 (1997).ADSCrossRefGoogle Scholar
  16. [16]
    K. Rzązewski and W. Zakowicz, J. Phys. B 25, L319 (1992).ADSCrossRefGoogle Scholar
  17. [17]
    T. Pfau et al., Phys. Rev. Lett., 73, 1223 (1994).ADSCrossRefGoogle Scholar
  18. [18]
    M. S. Chapman et al., Phys. Rev. Lett., 75, 3783 (1995).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • J. H. Eberly
    • 1
  • K. W. Chan
    • 1
  • C. K. Law
    • 1
    • 2
  1. 1.Center for Quantum Information and Department of Physics and AstronomyUniversity of RochesterRochesterUSA
  2. 2.Department of PhysicsThe Chinese University of Hong Kong, NTHong Kong SARChina

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