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Quantum probability from decision theory?

Barnum, H. and Caves, C. M. and Finkelstein, J. and Fuchs, C. A. and Schack, R. (2000) Quantum probability from decision theory? Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 456 (1997). pp. 1175-1182. ISSN 1364-5021. doi:10.1098/rspa.2000.0557.

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In a recent paper, Deutsch claims to derive the ‘probabilistic predictions of quantum theory’ from the ‘non–probabilistic axioms of quantum theory’ and the ‘nonprobabilistic part of classical decision theory.’ We show that his derivation includes a crucial hidden assumption that vitiates the force of his argument. Furthermore, we point out that in classical decision theory a standard set of non–probabilistic axioms is already sufficient to endow possible outcomes with a natural probability structure. Within that context we argue that Gleason's theorem, relying on fewer assumptions than Deutsch, provides a compelling derivation of the quantum probability law.

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Additional Information:© 2000 The Royal Society. Received 13 July 1999; revised 11 November 1999; accepted 10 December 1999. This work was supported in part by the the US Office of Naval Research (grant no. N00014-1-93-0116) and the US National Science Foundation (grant no. PHY-9722614). H.B. is partly supported by the Institute for Scientific Interchange Foundation (ISI) and Elsag-Bailey, and C.A.F. acknowledges the support of the Lee A. DuBridge Prize Postdoctoral Fellowship at Caltech. C.M.C., C.A.F. and R.S. thank the Isaac Newton Institute for its hospitality, H.B. thanks the ISI for its hospitality, and J.F. acknowledges the hospitality of Lawrence Berkeley National Laboratory.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-1-93-0116
Institute for Scientific Interchange FoundationUNSPECIFIED
Lee A. DuBridge FellowshipUNSPECIFIED
Subject Keywords:probability, decision theory, Gleason's theorem, quantum theory
Issue or Number:1997
Record Number:CaltechAUTHORS:20201215-170631438
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Official Citation:Barnum H., Caves C. M., Finkelstein J., Fuchs C. A. and Schack R. 2000. Quantum probability from decision theory? Proc. R. Soc. Lond. A. 456: 1175–1182.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107110
Deposited By: Rebecca Minjarez
Deposited On:17 Dec 2020 16:26
Last Modified:16 Nov 2021 18:59

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