QuantumBayesian Coherence (or, My Favorite Convex Set) Speaker(s): Chris Fuchs
Abstract: In a quantumBayesian delineation of quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurementoutcome probabilities from an objective quantum state. (A quantum system has potentially as many quantum states as there are agents considering it.) But what then is the role of the rule? In this paper, we argue that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, we show how to view the Born Rule as a normative rule in addition to usual Dutchbook coherence. It is a rule that takes into account how one should assign probabilities to the outcomes of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is seen particularly clearly by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete (SIC) measurement. We further explore the extent to which the general form of the new normative rule implies the full statespace structure of quantum mechanics. It seems to go some way.
Date: 13/08/2009  11:00 am
Collection: Reconstructing Quantum Theory  2009
