Foundations of Physics

, Volume 36, Issue 4, pp 512–525 | Cite as

Communication Complexity as a Principle of Quantum Mechanics

  • Adán CabelloEmail author


We introduce a two-party communication complexity problem in which the probability of success by using a particular strategy allows the parties to detect with certainty whether or not some forbidden communication has taken place. We show that theprobability of success is bounded by nature; any conceivable method which gives a probability of success outside these bounds is impossible. Moreover, any conceivable method to solve the problem which gives a probability success within these bounds is possible in nature. This example suggests that a suitaby chosen set of communication complexity problems could be the basis of an information-theoretic axiomatization of quantum mechanics.


Bell’s inequalities communication complexity foundations of quantum mechanics quantum communication quantum correlations Tsirelson’s inequalities 


03.65.Ud 03.65.Ta 


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  1. 1.
    Fuchs C.A., in Decoherence and its Implications in Quantum Computation and Information Transfer, Gonis A., and P. E. A. Turchi, eds. (IOS Press, Amsterdam, 2001).Google Scholar
  2. 2.
    Fuchs C.A., in Quantum Theory: Reconsideration of Foundations, Khrennikov A., ed. (Växjö University Press, Växjö, 2002).Google Scholar
  3. 3.
    Fuchs C.A. (2003). Notes on a Paulian Idea Fundational, Historical, Anecdotal and Forward-looking Thoughts on the Quantum. Selected Correspondence, 1995–2001. Växjö University Press, VäxjöGoogle Scholar
  4. 4.
    Fuchs C.A. (2003). J. Mod. Opt. 50: 987CrossRefzbMATHADSGoogle Scholar
  5. 5.
    Wheeler J.A., in Complexity, Entropy, and the Physics of Information, Zurek W.H., ed. (Addison-Wesley, Redwood City, California, 1990), p. 1.Google Scholar
  6. 6.
    Wheeler J.A., in Quantum Coherence and Reality, Anandan J., and Safko J.L., eds. (World Scientific, Singapore, 1995).Google Scholar
  7. 7.
    Wheeler J.A., and Ford K.W. (1998). Geons, Black Holes, and Quantum Foam. Norton W.W., New YorkzbMATHGoogle Scholar
  8. 8.
    Zeilinger A. (1999). Found. Phys 29:631CrossRefMathSciNetGoogle Scholar
  9. 9.
    Fuchs C.A., Fortschr. Phys. 46, 535 (1998). Reprinted in Quantum Computation: Where Do We Want To Go Tomorrow?, S.L. Braunstein ed. (Wiley-VCH, Weinheim, 1999), p. 229.Google Scholar
  10. 10.
    Fuchs C.A., in Quantum Communication, Computing, and Measurement, Kumar P., G. M. D’Ariano, and O. Hirota eds. (Kluwer, Dordrecht, 2000), p. 1.Google Scholar
  11. 11.
    Fuchs C.A., and Jacobs K. (2001). Phys. Rev. A 63:062305CrossRefADSGoogle Scholar
  12. 12.
    Brassard G., Comments during discussion at meeting “Quantum Foundations in the Light of Quantum Information and Cryptography,” Montreal, May 17–19, 2000.Google Scholar
  13. 13.
    Bennett C.H., and Brassard G. (1984). Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (Bangalore, India, 1984). IEEE, New York, p. 175Google Scholar
  14. 14.
    Lo H.-K., Chau H.F. (1999). Science 283:2050CrossRefPubMedADSGoogle Scholar
  15. 15.
    Brassard G., and C. Crépeau, in Advances in Cryptology: Proccedings of Crypto’90 (Springer-Verlag, Berlin, 1991) p. 49.Google Scholar
  16. 16.
    Mayers D. (1997). Phys. Rev. Lett. 78:3414CrossRefADSGoogle Scholar
  17. 17.
    Lo H.-K., Chau H.F. (1997). Phys. Rev. Lett 78:3410CrossRefADSGoogle Scholar
  18. 18.
    Clifton R., Bub J., and Halvorson H. (2003). Found. Phys 33:1561CrossRefMathSciNetGoogle Scholar
  19. 19.
    Smolin J.A. (2005). Quant. Inf. Comp. 5:161MathSciNetzbMATHGoogle Scholar
  20. 20.
    Spekkens R.W., unpublished, reported in Ref. 19.Google Scholar
  21. 21.
    Halvorson H., and Bub J. (2005). Quant. Inf. Comp. 5:170MathSciNetzbMATHGoogle Scholar
  22. 22.
    Bell J.S. (1964). Physics 1:195Google Scholar
  23. 23.
    Einstein A., Podolsky B., and Rosen N. (1935). Phys. Rev. 47:777CrossRefzbMATHADSGoogle Scholar
  24. 24.
    Bohm D. (1951). Quantum Theory. Prentice-Hall, Englewood Cliffs, New JerseyGoogle Scholar
  25. 25.
    Clauser J.F., Horne M.A., Shimony A., and Holt R.A. (1969). Phys. Rev. Lett. 23:880CrossRefADSGoogle Scholar
  26. 26.
    Froissart M. (1981). Nuovo Cimento Soc. Ital. Fis. 64B:241CrossRefADSMathSciNetGoogle Scholar
  27. 27.
    Fine A. (1982). Phys. Rev. Lett. 48:291CrossRefADSMathSciNetGoogle Scholar
  28. 28.
    Fine A. (1982). J. Math. Phys. 23:1306CrossRefADSMathSciNetGoogle Scholar
  29. 29.
    Popescu S., and Rohrlich D. (1994). Found Phys 24:379CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    Cleve R., and Buhrman H. (1997). Phys. Rev. A 56:1201CrossRefADSGoogle Scholar
  31. 31.
    Buhrman H., Cleve R., and Wigderson A., in Proceedings of the 30th Annual ACM Symposium on the Theory of Computing (ACM Press, New York, 1998), p. 63.Google Scholar
  32. 32.
    Buhrman H., van Dam W., Høyer P., Tapp A. (1999). Phys. Rev. A 60:2737CrossRefADSGoogle Scholar
  33. 33.
    Raz R., in Proceedings of the 31st Annual ACM Symposium on the Theory of Computing (ACM Press, New York, 1999), p. 358.Google Scholar
  34. 34.
    Steane A.M., and van Dam W. (2000). Phys. Today 53(2):35CrossRefGoogle Scholar
  35. 35.
    Buhrman H., Cleve R., and van Dam W. (2001). SIAM J. Comput 30:1829CrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    Brassard G., Broadbent A., and Tapp A., in Algorithms and Data Structures: Proceedings of 8th International Workshop, WADS 2003, Lecture Notes in Computer Science 2748, Denne F., Sack J.R., and Smid M., eds. (Springer, New York, 2003), P.1.Google Scholar
  37. 37.
    Brassard G. (2003). Found. Phys 33:1593CrossRefMathSciNetGoogle Scholar
  38. 38.
    Brassard G., Broadbent A., and Tapp A. (2005). Found. Phys 35:1877CrossRefzbMATHADSMathSciNetGoogle Scholar
  39. 39.
    Brassard G., Broadbent A., and Tapp A. (2005). Quant. Inf. Comp. 5:538zbMATHGoogle Scholar
  40. 40.
    Brassard G., Méthot A.A., Tapp A. (2005). Quant. Inf. Comp 5:275zbMATHGoogle Scholar
  41. 41.
    Mermin N.D. (1990). Phys. Today 43(6):9CrossRefGoogle Scholar
  42. 42.
    Mermin N.D. (1990). Am. J. Phys 58:731CrossRefADSMathSciNetGoogle Scholar
  43. 43.
    Mermin N.D. (1990). Phys. Rev. Lett. 65:3373CrossRefPubMedzbMATHADSMathSciNetGoogle Scholar
  44. 44.
    Greenberger D.M., Horne M.A., and Zeilinger A., in Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos ed. (Kluwer Academic, Dordrecht, 1989), p. 69.Google Scholar
  45. 45.
    Greenberger D.M., Horne M.A., Shimony A., and Zeilinger A. (1990). Am. J. Phys 58:1131CrossRefADSMathSciNetGoogle Scholar
  46. 46.
    Cabello A. (2001). Phys. Rev. Lett. 86:1911CrossRefPubMedADSMathSciNetGoogle Scholar
  47. 47.
    Cabello A. (2001). Phys. Rev. Lett. 87:010403CrossRefPubMedADSMathSciNetGoogle Scholar
  48. 48.
    Aravind P.K. (2002). Found. Phys. Lett. 15:397CrossRefMathSciNetGoogle Scholar
  49. 49.
    Aravind P.K. (2004). Am. J. Phys. 72:1303CrossRefADSMathSciNetGoogle Scholar
  50. 50.
    Vaidman L. (2001). Phys. Lett. A 286:241CrossRefzbMATHADSMathSciNetGoogle Scholar
  51. 51.
    Brukner Č., Żukowski M., Pan J.W., Zeilinger A. (2004). Phys. Rev. Lett 92:127901CrossRefPubMedADSMathSciNetGoogle Scholar
  52. 52.
    Tsirelson B.S., Zapiski LOMI 142, 174 (1985); English version: J. Soviet Math. 36, 557 (1987).Google Scholar
  53. 53.
    Landau L.J. (1988). Found. Phys 18:449CrossRefADSMathSciNetGoogle Scholar
  54. 54.
    Tsirelson B.S. (1993). Hadronic. J. Suppl 8:329MathSciNetzbMATHGoogle Scholar
  55. 55.
    Tsirelson B.S. (1980). Lett Math Phys 4:93CrossRefADSMathSciNetGoogle Scholar
  56. 56.
    Khalfin L.A., and Tsirelson B.S., in Symposium on the Foundations of Modern Physics: 50 Years of the Einstein-Podolsky-Rosen Experiment, Lahti P., and Mittelstaedt P., eds. (World Scientific, Singapore, 1985), p. 441.Google Scholar
  57. 57.
    Landau L.J. (1987). Phys. Lett. A 120:54CrossRefADSMathSciNetGoogle Scholar
  58. 58.
    Khalfin L.A., and Tsirelson B.S. (1992). Found. Phys 22:879CrossRefADSMathSciNetGoogle Scholar
  59. 59.
    Mermin N.D. (1981). Am. J. Phys 49:940CrossRefADSGoogle Scholar
  60. 60.
    Barrett J., Linden N., Massar S., Pironio S., Popescu S., and Roberts D. (2005). Phys. Rev. A 71:022101CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Departamento de Física Aplicada IIUniversidad de SevillaSevillaSpain

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