Quantum-Bayesian Coherence: The No-Nonsense Version

TL;DR

This paper presents a clear interpretation of the Born Rule within Quantum-Bayesianism, viewing it as an empirical normative rule that guides probability assignments based on prior and counterfactual measurements, especially using SIC representations.

Contribution

It offers a no-nonsense, probabilistic interpretation of the Born Rule as an empirical addition to Bayesian reasoning, emphasizing its normative role in quantum probability assignments.

Findings

Born Rule as a normative rule for probability assignment

Representation of quantum states via SIC measurements

Implications for quantum state-space structure

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, 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 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 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.