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Abstract: In a quantum-Bayesian take on quantum mechanics, the Born Rule cannot beinterpreted as a rule for setting measurement-outcome probabilities from anobjective quantum state. But if not, what is the role of the rule? In thispaper, we argue that it should be seen as an empirical addition to Bayesianreasoning itself. Particularly, we show how to view the Born Rule as anormative rule in addition to usual Dutch-book coherence. It is a rule thattakes into account how one should assign probabilities to the consequences ofvarious intended measurements on a physical system, but explicitly in terms ofprior probabilities for and conditional probabilities consequent upon theimagined outcomes of a special counterfactual reference measurement. Thisinterpretation is seen particularly clearly by representing quantum states interms of probabilities for the outcomes of a fixed, fiducial symmetricinformationally complete SIC measurement. We further explore the extent towhich the general form of the new normative rule implies the full state-spacestructure of quantum mechanics. It seems to get quite far.

Author: Christopher A. Fuchs, Ruediger Schack

Source: https://arxiv.org/


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