Quantum probabilities as degrees of belief

Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

Volumn 38, Issue 2, 2007, Pages 232-254

  Bub, Jeffrey ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

Bayes' rule; Projection postulate; Quantum foundations; Quantum information; Quantum measurement; Quantum probabilities

Indexed keywords

EID: 34250014200     PISSN: 13552198     EISSN: 18792502     Source Type: Journal    
DOI: 10.1016/j.shpsb.2006.09.002     Document Type: Article

References (35)

1. Bell J.S. Against measurement. Physics World 8 (1990) 33-40 [reprinted In Arthur Miller (Ed.), Sixty-two years of uncertainty: Historical, philosophical and physical inquiries into the foundations of quantum mechanics, New York: Plenum, pp. 17-31].
2. Bohm D. A suggested interpretation of quantum theory in terms of 'hidden' variables. i and ii. Physical Review 85 (1952) 166-193
3. Bondi H. Relativity and common sense (1980), Dover Publications, New York
4. Bub J. Von Neumann's projection postulate as a probability conditionalization rule in quantum mechanics. Journal of Philosophical Logic 6 (1977) 381-390
5. Bub, J. (2006). Quantum information and computation. In Handbook of philosophy of physics. Amsterdam: North-Holland, arXiv e-print quant-ph/0512125.
6. Caves C.M., Fuchs C.A., and Schack R. Quantum probabilities as Bayesian probabilities. Physical Review A 65 (2002) 022305
7. de Finetti B. Foresight: It's logical laws its subjective sources. In: Kyburg H., and Smokler H. (Eds). Studies in subjective probability (1964), Wiley, New York 93-159
8. Dieks D. Communication by EPR devices. Physics Letters A 92 (1982) 271-272
9. DiSalle R. Understanding space-time (2006), Cambridge University Press, Cambridge
10. Everett H. 'Relative state' formulation of quantum mechanics. Reviews of Modern Physics 29 (1957) 454-462
11. Feynman R.P. The character of physical law (1967), MIT Press, Cambridge, MA [first published in 1965 by the British Broadcasting Corporation].
12. Fuchs, C. A. (2001a). Notes on a Paulian idea: Foundational, historical, anecdotal and forward-looking thoughts on the quantum. arXiv e-print quant-ph/0105039.
13. Fuchs, C. A. (2001b). Quantum foundations in the light of quantum information. In A. Gonis (Ed.). Proceedings of the NATO advanced research workshop on decoherence and its implications in quantum computation and information transfer. arXiv e-print quant-ph/0106166.
14. Fuchs, C. A. (2002a). The anti-Växjo interpretation of quantum mechanics. arXiv e-print quant-ph/0204146.
15. Fuchs, C. A. (2002b). Quantum mechanics as quantum information (and only a little more). arXiv e-print quant-ph/0205039.
16. Galavotti M.C. The notion of subjective probability in the work of Ramsey and de Finetti. Theoria LVII 3 (1991) 239-259
17. Ghirardi, G. -C. (2002). Collapse theories. In E. Zalta (Ed.). The Stanford encyclopedia of philosophy. 〈http://plato.stanford.edu/entries/qm-collapse/〉.
18. Gleason A. Measures on the closed sub-spaces of hilbert spaces. Journal of Mathematics and Mechanics 6 (1957) 885-893
19. Goldstein, S. (2001). Bohmian mechanics. In E. Zalta (Ed.). The Stanford encyclopedia of philosophy. 〈http://plato.stanford.edu/entries/qm-bohm〉.
20. Goldstein, S., Lebowitz, J. L., Tumulka, R., & Zanghi, N. (2005). Canonical typicality. arXiv e-print quant-ph/0511091.
21. Henderson, L. (2007). Quantum measurement as Bayesian updating. In A. Bokulich (Ed.). Foundations of quantum information and entanglement.
22. Howson, C. (1990). Ramsey's big idea. In D. H. Mellor (Ed.). F.P. Ramsey: Philosophical papers. Cambridge: Cambridge University Press.
23. Howson C. Probability and logic. Journal of Applied Logic 1 (2003) 151-165
24. Hughston L.P., Jozsa R., and Wootters W.K. A complete classification of quantum ensembles having a given density matrix. Physics Letters A 183 (1993) 14-18
25. Nielsen M.A., and Chuang I. Quantum computation and quantum information (2000), Cambridge University Press, Cambridge
26. Palge, V., & Konrad, T. (2006). A remark on Fuchs' Bayesian interpretation of quantum mechanics. arXiv e-print.
27. Pitowsky, I. (2002). Betting on the outcomes of measurements: A Bayesian theory of quantum probability. arXiv e-print quant-ph/0208121.
28. Pitowsky, I. (2007). Quantum mechanics as a theory of probability. In W. Demopoulos, & I. Pitowsky (Eds.). Festschrift in honor of Jeffrey Bub. Western Ontario Series in Philosophy of Science. New York: Springer, arXiv e-print quantph/0510095.
29. Popescu S., and Rhorlich D. Nonlocality as an axiom. Foundations of Physics 24 (2005) 379
30. Popescu, S., Short, A. J., & Winter, A. (2005). Entanglement and the foundations of statistical mechanics. arXiv e-print quant-ph/0511225.
31. Ramsey, F. P. (1931). Truth and probability. In The foundations of mathematics and other logical essays. London: Routledge and Kegan Paul (pp. 156-199).
32. Schack R., Brun T.A., and Caves C.M. Quantum Bayes rule. Physical Review A 64 (2001) 014305-014308
33. Shannon, C. E. (1948). A mathematical theory of computation. Bell System Technical Journal 27, 379-423, 623-656.
34. Wallace D., and Brown H. Solving the measurement problem: de-Broglie-Bohm loses out to Everett. Foundations of Physics 35 (2005) 517-540
35. Wootters W.K., and Zurek W.H. A single quantum cannot be cloned. Nature 299 (1982) 802-803