Quantum-Bayesian Coherence

TL;DR

This paper presents a Bayesian interpretation of the Born Rule in quantum mechanics, viewing it as an empirical normative rule that guides probability assignments based on counterfactual measurements, especially using SIC representations.

Contribution

It introduces a novel Bayesian perspective on the Born Rule as an empirical normative addition to coherence, utilizing SIC measurements to interpret quantum states.

Findings

The Born Rule can be seen as a normative rule for probability assignments.

Representation of quantum states via SIC measurements clarifies the rule's role.

The normative rule implies significant aspects of quantum state-space structure.

Abstract

In a quantum-Bayesian take on quantum mechanics, 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. It seems to get quite far.