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Quantum-Bayesian coherence

Christopher A. Fuchs* and Rüdiger Schack

Christopher A. Fuchs*

  • Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada and Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University, Stellenbosch 7600, South Africa

Rüdiger Schack

  • Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom and Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University, Stellenbosch 7600, South Africa

  • *Current address: Raytheon BBN Technologies, 10 Moulton Street, Cambridge, MA 02138, USA.
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Rev. Mod. Phys. 85, 1693 – Published 27 December, 2013

DOI: https://doi.org/10.1103/RevModPhys.85.1693

Abstract

In the quantum-Bayesian interpretation of quantum theory (or QBism), the Born rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, the argument is given that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, it is shown 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 consequences 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 exemplified by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete measurement. The extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics is explored.

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Rev. Mod. Phys. 85, 1693– Published 27 December, 2013
  • Received 9 August 2009

© 2013 American Physical Society

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