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Foundations of Physics

, Volume 33, Issue 11, pp 1561–1591 | Cite as

Characterizing Quantum Theory in Terms of Information-Theoretic Constraints

  • Rob Clifton
  • Jeffrey Bub
  • Hans Halvorson
Article

Abstract

We show that three fundamental information-theoretic constraints—the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment—suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment.

quantum theory information-theoretic constraints 

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References

  1. 1.
    A. Aspect, J. Dalibard, and G. Roger, “Experimental tests of Bell's inequalities using time-varying analyzers”, Phys. Rev. Lett. 49, 1804–1807 (1982).Google Scholar
  2. 2.
    A. Arageorgis, J. Earman, and L. Ruetsche, “Weyling the time away: The non-unitary implementability of quantum field dynamics on curved space-time”, Stud. Hist. Philos. Modern Phys. 33, 151–184 (2002).Google Scholar
  3. 3.
    G. Bacciagaluppi, “Separation theorems and Bell inequalities in algebraic quantum mechanics”, in Symposium on the Foundations of Modern Physics 1993: Quantum Measurement, Irreversibility and the Physics of Information, P. Busch, P. Lahti, and P. Mittelstaedt, eds. (World Scientific, Singapore, 1994), pp. 29–37.Google Scholar
  4. 4.
    H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher, “Non-commuting mixed states cannot be broadcast”, Phys. Rev. Lett. 76, 2318(1996).Google Scholar
  5. 5.
    C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing, ” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, pp. 175–179, IEEE, 1984.Google Scholar
  6. 6.
    P. Bóna, “Extended quantum mechanics”, Acta Phys. Slovaca 50(1), 1–198 (2000).Google Scholar
  7. 7.
    G. Brassard, comments during discussion at meeting “Quantum foundations in the light of quantum information and cryptography, ” Montreal, May 17–19, 2000.Google Scholar
  8. 8.
    O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics (Springer, New York, 1996).Google Scholar
  9. 9.
    J. Bub, “The quantum bit commitment theorem”, Found. Phys. 31, 735–756 (2001).Google Scholar
  10. 10.
    P. Busch and J. Singh, “Lüders' theorem for unsharp quantum measurements”, Phys. Lett. A 249, 10–12 (1998).Google Scholar
  11. 11.
    R. Clifton and H. Halvorson, “Entanglement and open systems in algebraic quantum field theory”, Stud. Hist. Philos. Modern Phys. 32, 1–31 (2001).Google Scholar
  12. 12.
    R. Clifton and H. Halvorson, “Are Rindler quanta real? Inequivalent particle concepts in quantum field theory”, Brit. J. Philos. Sci. 52, 417–470.Google Scholar
  13. 13.
    A. Connes, Noncommutative Geometry (Academic, San Diego, 1994).Google Scholar
  14. 14.
    D. Deutsch, “It from qubit, ” in Science and Ultimate Reality, J. Barrow, P. Davies, and C. Harper, eds. (Cambridge University Press, Cambridge, 2003).Google Scholar
  15. 15.
    D. Dieks, “Communication by EPR devices”, Phys. Lett. A 92(6), 271–271 (1982).Google Scholar
  16. 16.
    R. Duvenhage, “Recurrence in quantum mechanics”, quant-ph/0202023.Google Scholar
  17. 17.
    R. Duvenhage, “The nature of information in quantum mechanics”, quant-ph/0203070.Google Scholar
  18. 18.
    A. Einstein, “What is the theory of relativity. ” First published in The Times, London, November 28, 1919, p. 13. Also published under the title “Time, space and gravitation”, in Optician, The British Optical Journal 58, 187–188 (1919).Google Scholar
  19. 19.
    A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).Google Scholar
  20. 20.
    A. Einstein, “Autobiographical notes”, in Albert Einstein: Philosopher-Scientist, (The Library of Living Philosophers, Vol. VII), P. A. Schilpp, ed. (Open Court, La Salle, IL, 1949).Google Scholar
  21. 21.
    G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley, New York, 1973).Google Scholar
  22. 22.
    M. Florig and S. Summers, “On the statistical independence of algebras of observables”, J. Math. Phys. 38, 1318–1328 (1997).Google Scholar
  23. 23.
    C. A. Fuchs, “Information gain vs. state disturbance in quantum theory”, Fortschr. Phys. 46(4, 5), 535–565. Reprinted in Quantum Computation: Where Do We Want to Go Tomorrow?, S. L. Braunstein, ed. (Wiley-VCH, Weinheim, 1999), pp. 229–259.Google Scholar
  24. 24.
    C. A. Fuchs, “Just two nonorthogonal quantum states, ” in Quantum Communication, Computing, and Measurement 2, P. Kumar, G. M. D'Ariano, and O. Hirota, eds. (Kluwer Academic, Dordrecht, 2000), pp. 11–16.Google Scholar
  25. 25.
    C. A. Fuchs and K. Jacobs, “An information tradeoff relation for finite-strength quantum measurements”, Phys. Rev. A 63, 062305(2001).Google Scholar
  26. 26.
    W. H. Furry, “A note on the quantum mechanical theory of measurement”, Phys. Rev. 49, 393–399 (1936).Google Scholar
  27. 27.
    N. Gisin, Helv. Phys. Acta 62, 363–371 (1989).Google Scholar
  28. 28.
    L. P. Hughston, R. Jozsa, and W. K. Wootters, “A complete classification of quantum ensembles having a given density matrix”, Phys. Lett. A 183, 14–18 (1993).Google Scholar
  29. 29.
    E. T. Jaynes, “Information theory and statistical mechanics II”, Phys. Rev. 108(2), 171–190 (1957).Google Scholar
  30. 30.
    R. Kadison and J. Ringrose, Fundamentals of the Theory of Operator Algebras (American Mathematical Society, Providence, RI, 1997).Google Scholar
  31. 31.
    B. O. Koopman, “Hamiltonian systems and transformations in Hilbert space”, Proc. Nat. Acad. Sci. USA 17, 315–318 (1931).Google Scholar
  32. 32.
    L. J. Landau, “On the violation of Bell's inequality in quantum theory”, Phys. Lett. A 120, 54–56 (1987).Google Scholar
  33. 33.
    L. J. Landau, “Experimental tests of distributivity”, Lett. Math. Phys. 25, 47–50 (1992).Google Scholar
  34. 34.
    N. Landsman, Mathematical Topics Between Classical and Quantum Mechanics (Springer, New York, 1998).Google Scholar
  35. 35.
    H.-K. Lo and H. F. Chau, “Is quantum bit commitment really possible?”, Phys. Rev. Lett. 78, 3410–3413 (1997).Google Scholar
  36. 36.
    D. Mauro, “On Koopman–von Neumann waves”, quant-ph/0105112.Google Scholar
  37. 37.
    D. Mayers, “Unconditionally secure quantum bit commitment is impossible”, in Proceedings of the Fourth Workshop on Physics and Computation (New England Complex System Institute, Boston, 1996), pp. 224–228.Google Scholar
  38. 38.
    D. Mayers, “Unconditionally secure quantum bit commitment is impossible”, Phys. Rev. Lett. 78, 3414–3417 (1997).Google Scholar
  39. 39.
    A. Petersen, “The philosophy of Niels Bohr”, B. Atom. Sci. 19(7), 8–14 (1963).Google Scholar
  40. 40.
    R. Powers and E. Størmer, “Free states of the canonical anticommutation relations”, Comm. Math. Phys. 16, 1–33 (1970).Google Scholar
  41. 41.
    J. Roberts and G. Roepstorff, “Some basic concepts of algebraic quantum theory”, Comm. Math. Phys. 11, 321–338 (1969).Google Scholar
  42. 42.
    H. Roos, “Independence of local algebras in quantum field theory”, Comm. Math. Phys. 16, 238–246 (1970).Google Scholar
  43. 43.
    E. Schrödinger, “Discussion of probability relations between separated systems”, Proc. Camb. Philos. Soc. 31, 555–563 (1935).Google Scholar
  44. 44.
    E. Schrödinger, “Probability relations between separated systems”, Proc. Camb. Philos. Soc. 32, 446–452 (1936).Google Scholar
  45. 45.
    I. Segal, “Postulates for general quantum mechanics”, Ann. Math. 48, 930–948 (1947).Google Scholar
  46. 46.
    S. Summers, “On the independence of local algebras in quantum field theory”, Rev. Math. Phys. 2, 201–247 (1990).Google Scholar
  47. 47.
    J. von Neumann, Ann. Math. 33, 587, 789 (1932).Google Scholar
  48. 48.
    W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned”, Nature 299, 802–803 (1982).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Rob Clifton
    • 1
  • Jeffrey Bub
    • 2
  • Hans Halvorson
    • 3
  1. 1.Department of PhilosophyUniversity of PittsburghPittsburgh
  2. 2.Department of PhilosophyUniversity of MarylandCollege Park
  3. 3.Department of PhilosophyPrinceton UniversityPrinceton

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