Derivation of the Born Rule from Operational Assumptions

TL;DR

This paper derives the Born rule from operational assumptions in quantum mechanics, applicable even with limited probability definitions, and connects with decision theory approaches like Everett's interpretation.

Contribution

It provides a novel derivation of the Born rule that does not rely on state normalization and extends to foundational quantum approaches.

Findings

Derivation applies with only a single resolution of the identity

Connects operational assumptions with decision theory approaches

Applicable across major foundational quantum frameworks

Abstract

The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it applies to all the major foundational approaches to quantum mechanics. There are important points of contact with Deutsch's program for deducing the probabilistic interpretation of quantum mechanics from decision thoery, as recently completed by Wallace. Decision theory can be used to supplement the present derivation, in application to the Everett interpretation, but it is otherwise unnecessary.