A Quantum-Bayesian Route to Quantum-State Space |
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Authors: | Christopher A Fuchs Rüdiger Schack |
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Institution: | 1.Perimeter Institute for Theoretical Physics,Waterloo,Canada;2.Department of Mathematics, Royal Holloway,University of London,Egham, Surrey,UK |
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Abstract: | In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist
Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability
rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper,
we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum
Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement
or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability.
We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification
of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor. |
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