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  • Open Access

Beyond the projection postulate and back: Quantum theories with generalized state-update rules

Vincenzo Fiorentino*,† and Stefan Weigert*,‡

  • *These authors contributed equally to this work.
  • †Contact author: vincenzo.fiorentino@york.ac.uk
  • ‡Contact author: stefan.weigert@york.ac.uk
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Phys. Rev. A 113, 012204 – Published 2 January, 2026

DOI: https://doi.org/10.1103/2zpm-jsh7

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 Lüders rule. Among other basic properties, any prospective rule must define unique post-measurement states and not allow for superluminal signaling. 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.

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Phys. Rev. A 113, 012204– Published 2 January, 2026
  • Received 26 August 2025
  • Accepted 5 December 2025
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