Decoherence, Branching, and the Born Rule in a Mixed-State Everettian Multiverse

TL;DR

This paper extends the Everettian quantum mechanics framework to mixed states, developing decoherence and branching concepts, and providing a unified approach to classical and quantum probabilities within the multiverse.

Contribution

It introduces a conceptual foundation for decoherence and branching in a mixed-state multiverse, expanding Born rule justifications beyond pure states.

Findings

Unified classical and quantum probabilities in Everettian multiverse

Extended Born rule justifications to mixed states

Framework supports decoherence and branching in mixed states

Abstract

In Everettian quantum mechanics, justifications for the Born rule appeal to self-locating uncertainty or decision theory. Such justifications have focused exclusively on a pure-state Everettian multiverse, represented by a wave function. Recent works in quantum foundations suggest that it is viable to consider a mixed-state Everettian multiverse, represented by a (mixed-state) density matrix. Here, we develop the conceptual foundations for decoherence and branching in a mixed-state multiverse, and extend arguments for the Born rule to this setting. This extended framework provides a unification of 'classical' and 'quantum' probabilities, and additional theoretical benefits, for the Everettian picture.