Quantum-Bayesian Coherence (or, My Favorite Convex Set)

          @misc{ pirsa_PIRSA:09080018,
            doi = {10.48660/09080018},
            url = {https://pirsa.org/09080018},
            author = {Fuchs, Chris},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantum-Bayesian Coherence (or, My Favorite Convex Set)},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {aug},
            note = {PIRSA:09080018 see, \url{https://pirsa.org}}
          }
          

Abstract

In a quantum-Bayesian delineation of quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome 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 Dutch-book 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 state-space structure of quantum mechanics. It seems to go some way.