Betting on the Outcomes of Measurements:A Bayesian Theory of Quantum Probability

The Bayesian approach takes probability to be a measure of ignorance, reflecting our state of knowledge and not merely the state of the world. It follows Ramsey’s contention that “we have the authority both of ordinary language and of many great thinkers for discussing under the heading of probability… the logic of partial belief” (Ramsey 1926. Truth and probability. Cambridge: Cambridge University Press, p. 55). Here we shall assume, furthermore, that probabilities are revealed in rational betting behavior: “The old-established way of measuring a person’s belief … by proposing a bet, and see what are the lowest odds which he will accept, is fundamentally sound.” My aim is to provide an account of the peculiarities of quantum probability in this framework. The approach is intimately related to and inspired by the foundational work on quantum information of Fuchs (2001, Quantum mechanics as quantum information (and only a little more). Quant-ph 0205039), Schack et al. (2001, Physical Review A64 014305: 1–4) and Caves et al. (2002, Physical Review A 65(2305): 1–6).

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