Subjective probability and quantum certainty

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

Volumn 38, Issue 2, 2007, Pages 255-274

  Caves, Carlton M ^a   Fuchs, Christopher A ^b   Schack, Rüdiger ^c  

^a UNIVERSITY OF NEW MEXICO   (United States)

^b LUCENT TECHNOLOGIES   (United States)

^c UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Certainty; Copenhagen interpretation; de Finetti; State preparation; Subjective probability

Indexed keywords

EID: 34250005780     PISSN: 13552198     EISSN: 18792502     Source Type: Journal    
DOI: 10.1016/j.shpsb.2006.10.007     Document Type: Article

References (67)

1. Appleby D.M. Facts, values and quanta. Foundations of Physics 35 (2005) 627
2. Appleby D.M. Probabilities are single-case, or nothing. Optics Spectrum 99 (2005) 447
3. Berger J.O., and Sellke T. Testing a point null hypothesis: The irreconcilability of P-values and evidence. Journal of the American Statistical Association 82 (1987) 112
4. Bernardo J.M., and Smith A.F.M. Bayesian theory (1994), Wiley, Chichester
5. Bohr, N. (1939). The causality problem in modern physics. In New theories in physics (pp. 11-45). Paris: International Institute of Intellectual Cooperation.
6. Braithwaite R.B. Scientific explanation (1968), Cambridge University Press, Cambridge
7. Brown H.R., and Svetlichny G. Nonlocality and Gleason's lemma. Part I. Deterministic theories. Foundations of Physics 20 (1990) 1379
8. Brukner C., and Zeilinger A. Conceptual inadequacy of the Shannon information in quantum measurements. Physical Review A 63 (2001) 022113
9. Brun T.A., Caves C.M., and Schack R. Quantum Bayes rule. Physical Review A 63 (2001) 042309
10. Busch P. Classical versus quantum ontology. Studies in History and Philosophy of Modern Physics 33B (2002) 517
11. Caves C.M., Fuchs C.A., and Schack R. Conditions for compatibility of quantum-state assignments. Physical Review A 66 (2002) 062111
12. Caves C.M., Fuchs C.A., and Schack R. Unknown quantum states: The quantum de Finetti representation. Journal of Mathematical Physics 43 (2002) 4537
13. Caves C.M., Fuchs C.A., and Schack R. Quantum probabilities as Bayesian probabilities. Physical Review A 65 (2002) 022305
14. Caves C.M., and Schack R. Properties of the frequency operator do not imply the quantum probability postulate. Annals of Physics 315 (2005) 123 [corrigendum: Annals of Physics, 321, 504]
15. In: Cohen R.S., and Stachel J.J. (Eds). Selected papers of Léon Rosenfeld (1979), D. Reidel, Dordrecht
16. D'Ariano G.M., Maccone L., and Lo Presti P. Quantum calibration of measuring apparatuses. Physical Review Letters 93 (2004) 250407
17. de Finetti B. Probabilismo. Logos 14 (1931) 163 translation: Probabilism. Erkenntnis, 31, 169-223.
18. de Finetti B. Theory of probability (1990), Wiley, New York
19. Faye J. Niels Bohr: His heritage and legacy. An antirealist view of quantum mechanics (1991), Kluwer, Dordrecht
20. In: Faye J., and Folse H.J. (Eds). Niels Bohr and contemporary philosophy (1994), Kluwer, Dordrecht
21. Feller W. An introduction to probability theory and its applications. Vol. I, 3rd ed. (1968), Wiley, New York
22. Folse H.J. The philosophy of Niels Bohr: The framework of complementarity (1985), North-Holland, Amsterdam
23. Fuchs, C. A. (2002). Quantum mechanics as quantum information (and only a little more). e-print quant-ph/0205039 (see also C. A. Fuchs, Quantum mechanics as quantum information, mostly. Journal of Modern Optics, 50, 987, for an abridged version).
24. Fuchs C.A., and Schack R. Unknown quantum states and operations, a Bayesian view. In: Paris M.G.A., and Řeháček J. (Eds). Quantum estimation theory (2004), Springer, Berlin 151
25. Fuchs C.A., Schack R., and Scudo P.F. A de Finetti representation theorem for quantum process tomography. Physical Review A 69 (2004) 062305
26. Garrett A.J.M. Making sense of quantum mechanics: Why you should believe in hidden variables. In: Mohammed-Djafari A., and Demoment G. (Eds). Maximum entropy and Bayesian methods (Paris, France, 1992) (1993), Kluwer, Dordrecht 79-83
27. Giere R.N. Objective single-case probabilities and the foundations of statistics. In: Suppes P., Henkin L., Jojo A., and Moisil Gr.C. (Eds). Logic, methodology and philosophy of science IV (1973), North-Holland, Amsterdam 467-483
28. Giere R.N. Propensity and necessity. Synthese 40 (1979) 439-451
29. Grangier P. Contextual objectivity and the quantum formalism. International Journal of Quantum Information 3 (2005) 17-22
30. Heywood P., and Redhead M.L.G. Nonlocality and the Kochen-Specker paradox. Foundations of Physics 13 (1983) 481
31. Ismael, J. (2006). Chance reconsidered. Unpublished, preliminary draft.
32. Jammer M. The philosophy of quantum mechanics (1974), Wiley, New York and various references therein
33. Jaynes E.T. Information theory and statistical mechanics. Physical Review 106 (1957) 620
34. Jaynes E.T. Information theory and statistical mechanics. II. Physical Review 108 (1957) 171
35. Jeffrey R. Unknown probabilities. Erkenntnis 45 (1997) 327
36. Jeffrey R. Subjective probability. The real thing (2004), Cambridge University Press, Cambridge
37. Jeffreys H. Theory of probability. 3rd ed. (1961), Clarendon Press, Oxford
38. In: Kyburg Jr. H.E., and Smokler H.E. (Eds). Studies in subjective probability. 2nd ed. (1980), Robert E. Krieger Publishing, Huntington
39. Larsson J.-A. A Kochen-Specker inequality. Europhysics Letters 58 (2002) 799
40. Lehmann E.L. Testing statistical hypotheses. 2nd ed. (1986), Wiley, New York
41. Leifer M.S. Quantum dynamics as an analog of conditional probability. Physical Review A 74 (2006) 042310
42. Leifer, M. S. (2006b). Conditional density operators and the subjectivity of quantum operations. quant-ph/0611233.
43. Lewis, D. (1986a). A subjectivist's guide to objective chance. In Studies in inductive logic and probability (Vol. II, p. 83). Oxford: Oxford University Press.
44. Lewis, D. (1986b). Postscripts to 'A subjectivist's guide to objective chance. In Philosophical papers (Vol. II, p. 114). Oxford: Oxford University Press.
45. Loewer B. Determinism and chance. Studies in History and Philosophy of Modern Physics 32 (2001) 609
46. Loewer B. David Lewis' Humean theory of objective chance. Philosophy of Science 75 (2004) 1115
47. Mermin N.D. Is the moon there when nobody looks? Reality and the quantum theory. Physics Today April 1985 (1985) 38
48. Mermin N.D. Whose knowledge?. In: Bertlmann R., and Zeilinger A. (Eds). Quantum (Un)speakables: Essays in commemoration of John S. Bell (2002), Springer, Berlin 271
49. Mermin N.D. In praise of measurement. Quantum Information Processes 5 (2006) 239-260
50. Murdoch D. Niels Bohr's philosophy of physics (1987), Cambridge University Press, Cambridge
51. Nielsen M.A., and Chuang I.L. Quantum computation and quantum information (2000), Cambridge University Press, Cambridge
52. North, J. (2003). Understanding probabilities in statistical mechanics. Unpublished manuscript, available at 〈aardvark.ucsd.edu/grad_conference/north.doc〉.
53. Penrose R. The emperor's new mind (1989), Oxford University Press, New York
54. Peres A. What is a state vector?. American Journal of Physics 52 (1984) 644
55. Peres A. Quantum theory: concepts and methods (1993), Kluwer Academic Publishers, Dordrecht
56. Pitowsky I. Betting on the outcomes of measurements: A Bayesian theory of quantum probability. Studies in History and Philosophy of Modern Physics 34 (2003) 395
57. Plotnitsky A. Complementarity: Anti-epistemology after Bohr and Derrida (1994), Duke University Press, Durham, NC
58. Savage L.J. The foundations of statistics. 2nd ed. (1972), Dover, New York
59. Schack R. Quantum theory from four of Hardy's axioms. Foundations of Physics 33 (2003) 1461
60. Shalizi, C. R., & Moore, C. (2003). What is a macrostate? Subjective observations and objective dynamics. e-print cond-mat/0303625.
61. Spekkens R.W. Evidence for the epistemic view of quantum states: A toy theory. Physical Review A 75 (2007) 032110
62. Stairs A. Quantum logic, realism, and value-definiteness. Philosophy of Science 50 (1983) 578
63. Stapp H.P. The Copenhagen interpretation. American Journal of Physics 40 (1972) 1098
64. Suppes P. New foundations for objective probability: Axioms for propensities. In: Suppes P., Henkin L., Jojo A., and Moisil Gr.C. (Eds). Logic, methodology and philosophy of science IV (1973), North-Holland, Amsterdam 515-529
65. Timpson, C. G. (2006). Philosophical aspects of quantum information theory. e-print quant-ph/0611187. In D. Rickles (Ed.), The Ashgate companion to the new philosophy of physics (particularly Sections 3.3.1 and 5.2.3). Ashgate Publishing, to appear.
66. White A. Certainty. Proceedings of the Aristotelian Society 46 (1972) 1 (See also Wittgenstein, L. On Certainty. Malden, MA: Blackwell)
67. Wootters W.K. Quantum mechanics without probability amplitudes. Foundations of Physics 16 (1986) 391