Skip to main content
Log in

Quantum Theory from Four of Hardy's Axioms

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of “quantum theory from five reasonable axioms.” Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not necessary for his derivation. By reformulating Hardy's assumptions, and modifying a part of his proof, in terms of Bayesian probabilities, we show that his work can be easily reconciled with a Bayesian interpretation of quantum probability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Studies in Subjective Probability, 2nd edn., H. E. Kyburg and H. E. Smokler, eds. (Krieger Publishing, Huntington, NY, 1980).

    Google Scholar 

  2. J. M. Bernardo and A. F. M. Smith, Bayesian Theory (Wiley, Chichester, 1994).

    Google Scholar 

  3. C. M. Caves, C. A. Fuchs, and R. Schack, “Conditions for comp00atibility of quantum state assignments, ” Phys. Rev. A 66, 062111(2002).

    Google Scholar 

  4. D. Malakoff, “Bayes offers a ‘new’ way to make sense of numbers, ” Science 286, 1460(1999).

    Google Scholar 

  5. C. M. Caves, C. A. Fuchs, and R. Schack, “Quantum probabilities as Bayesian probabilities, ” Phys. Rev. A 65, 022305(2002).

    Google Scholar 

  6. C. M. Caves, C. A. Fuchs, and R. Schack, “Unknown quantum states: The quantum de Finetti representation, ” J. Math. Phys. 43, 4537(2002).

    Google Scholar 

  7. R. Schack, T. A. Brun, and C. M. Caves, “Quantum Bayes rule, ” Phys. Rev. A 64, 014305(2001).

    Google Scholar 

  8. T. A. Brun, C. M. Caves, and R. Schack, “Entanglement purification of unknown quantum states, ” Phys. Rev. A 63, 042309(2001).

    Google Scholar 

  9. L. Hardy, “Quantum theory from five reasonable axioms, ” e-print quant-ph/0101012 v4 (25 September 2001).

  10. L. Hardy, “Why quantum theory?, ” in Proceedings of the NATO Advanced Research Workshop on Modality, Probability, and Bell's theorem, J. Butterfield and T. Placek, eds. (IOS Press, Amsterdam, 2002); e-print quant-ph/0111068.

    Google Scholar 

  11. R. von Mises, Probability, Statistics, and Truth (Dover, New York, 1957).

    Google Scholar 

  12. B. C. van Fraassen, “Relative frequencies, ” Synthese 34, 133(1977).

    Google Scholar 

  13. E. T. Jaynes, Probability Theory (Cambridge University Press, Cambridge, 2003).

    Google Scholar 

  14. L. Hardy, private communication. See also remarks at the end of Sec. 6.1 of Ref. 9.

  15. C. A. Fuchs, “Quantum states: What the hell are they?, ” unpublished (2002), pp. 159-166, available at http://cm.bell-labs.com/who/cafuchs.

  16. C. A. Fuchs, “Quantum mechanics as quantum information (and only a little more), ” e-print quant-ph/0205039.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schack, R. Quantum Theory from Four of Hardy's Axioms. Foundations of Physics 33, 1461–1468 (2003). https://doi.org/10.1023/A:1026044329659

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026044329659

Navigation