Betting on the outcomes of measurements: a Bayesian theory of quantum probability
Abstract
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These include the uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics to it. We conclude with a philosophical discussion on the interpretation of quantum mechanics.DOI
10.1016/s1355-2198(03)00035-2
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Citations of this work
Subjective probability and quantum certainty.Carlton M. Caves, Christopher A. Fuchs & Rüdiger Schack - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):255-274.
QBism and the limits of scientific realism.David Glick - 2021 - European Journal for Philosophy of Science 11 (2):1-19.
Quantum probabilities as degrees of belief.Jeffrey Bub - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):232-254.
Quantum probability and many worlds.Meir Hemmo - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):333-350.
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