Journal of Statistical Physics

, Volume 108, Issue 1–2, pp 49–122 | Cite as

Entanglement and Properties of Composite Quantum Systems: A Conceptual and Mathematical Analysis

  • GianCarlo Ghirardi
  • Luca Marinatto
  • Tullio Weber


Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of the paper deals with composite systems in pure states. After a detailed discussion and a precise formal analysis of the case of systems of distinguishable particles, the problems of entanglement and the one of the properties of subsystems of systems of identical particles are thoroughly discussed. This part is the most interesting and new and it focuses in all details various subtle questions which have never been adequately discussed in the literature. Some inappropriate assertions which appeared in recent papers are analyzed. The relations of the main subject of the paper with the nonlocal aspects of quantum mechanics, as well as with the possibility of deriving Bell's inequality are also considered.

entanglement identical particles 


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  1. 1.
    E. Schrödinger, Naturwissenschaften 23:807 (1935); English translation in Proc. Am. Philos. Soc. 124:323 (1980).Google Scholar
  2. 2.
    D. Dürr, S. Goldstein, and N.Zanghí, J. Stat. Phys. 63:843 (1992).Google Scholar
  3. 3.
    A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47:777 (1935).Google Scholar
  4. 4.
    P. Eberhard, Nuovo Cimento B 46:392 (1978).Google Scholar
  5. 5.
    G. C. Ghirardi and T. Weber, Lettere Nuovo Cimento 26:599 (1979).Google Scholar
  6. 6.
    G. C. Ghirardi, A. Rimini, and T. Weber, Lettere Nuovo Cimento 27:293 (1980).Google Scholar
  7. 7.
    G. C. Ghirardi, R. Grassi, A. Rimini, and T. Weber, Europhys. Lett. 6:95 (1988).Google Scholar
  8. 8.
    P. Suppes and M. Zanotti, in Logic and Probability in Quantum Mechanics, P. Suppes, ed. (Reidel, Dordrecht, 1976), p. 445.Google Scholar
  9. 9.
    B. van Fraassen, Synthese 52:25 (1982).Google Scholar
  10. 10.
    J. Jarrett, Noûs 18:569 (1984).Google Scholar
  11. 11.
    A. Shimony, in Proceedings of the International Symposium on the Foundations of Quantum Mechanics, S. Kamefuchi et al., eds. (Physical Society of Japan, Tokyo, 1984), p. 225.Google Scholar
  12. 12.
    G. C. Ghirardi, A. Rimini, and T. Weber, Nuovo Cimento B 39:130 (1977).Google Scholar
  13. 13.
    G. C. Ghirardi, in Bell's Theorem and the Foundations of Modern Physics (World Scientific, Singapore, 1992).Google Scholar
  14. 14.
    G. C. Ghirardi, in Waves, Information and Foundations of Physics, R. Pratesi et al., eds. (Editrice Compositori-Società Italiana di Fisica, 1998).Google Scholar
  15. 15.
    G. C. Ghirardi, in Spin Statistics Connection and Commutation Relations, R. C. Hilborn et al., eds. (American Institute of Physics, 2000).Google Scholar
  16. 16.
    P. Teller, Philosophy of Science 50:309 (1983).Google Scholar
  17. 17.
    M. Readhead and P. Teller, British J. Philos. Sci. 43:201 (1992).Google Scholar
  18. 18.
    M. L. Dalla Chiara and G. Toraldo di Francia, in Bridging the gap: Philosophy, Mathematics, Physics, Corsi et al., eds. (Dordrecht, Kluwer Academic Publishers, 1993), p. 261.Google Scholar
  19. 19.
    N. Huggett, The Monist 80:118 (1997).Google Scholar
  20. 20.
    D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Quantum Interferometry: Proceedings of an Adriatico Workshop, F. de Martini et al., eds. (Trieste, 1996).Google Scholar
  21. 21.
    A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1962), Vol. 2, p. 600.Google Scholar
  22. 22.
    G. Krenn and A. Zeilinger, Phys. Rev. A 54:1793 (1996).Google Scholar
  23. 23.
    D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Bell's Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic Publishers, 1989).Google Scholar
  24. 24.
    G. C. Ghirardi, in Dynamical Systems and Microphysics, A. Blaquiere et al., eds. (Springer-Verlag, 1980).Google Scholar
  25. 25.
    M. Horne, A. Shimony and A. Zeilinger, in Quantum Coherence, J. S. Anandan, ed. (World Scientific, Singapore, 1991).Google Scholar
  26. 26.
    R. F. Werner, Phys. Rev. A 40:4277 (1989).Google Scholar
  27. 27.
    M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223:1 (1996).Google Scholar
  28. 28.
    A. Peres, Phys. Rev. Lett. 77:1413 (1996).Google Scholar
  29. 29.
    S. Teufel, K. Berndl, D. Dürr, S. Goldstein, and N. Zanghí, Phys. Rev. A 56:1217 (1997).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • GianCarlo Ghirardi
    • 1
    • 2
  • Luca Marinatto
    • 1
  • Tullio Weber
    • 1
  1. 1.Department of Theoretical Physics of the University of TriesteIstituto Nazionale di Fisica NucleareItaly
  2. 2.International Centre for Theoretical PhysicsTriesteItaly

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