Beyond the Projection Postulate and Back: Quantum Theories with Generalised State-Update Rules

TL;DR

This paper explores alternative, consistent state-update rules in quantum mechanics beyond the traditional projection postulate, analyzing their properties, constraints, and implications for the foundations of quantum theory.

Contribution

It systematically investigates hypothetical quantum state-update rules, providing explicit examples and operational criteria to distinguish them from the standard projection postulate.

Findings

Identifies valid alternative update rules that do not violate causality

Provides explicit examples of unconventional quantum state-update rules

Clarifies operational properties that differentiate the projection postulate from alternatives

Abstract

Are there consistent and physically reasonable alternatives to the projection postulate? Does it have unique properties compared with acceptable alternatives? We answer these questions by systematically investigating hypothetical state-update rules for quantum systems that nature could have chosen over the L\"uders rule. Among other basic properties, any prospective rule must define unique post-measurement states and not allow for superluminal signalling. Particular attention will be paid to consistently defining post-measurement states when performing local measurements in composite systems. Explicit examples of valid unconventional update rules are presented, each resulting in a distinct, well-defined foil of quantum theory. This framework of state-update rules allows us to identify operational properties that distinguish the projective update rule from all others and to put earlier derivations of the projection postulate into perspective.