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Sufficiency of the counterfactual account of Lüders' rule to rule out ontological models of quantum mechanics

Alisson Tezzin1,2,3,*, Bárbara Amaral1, and Jonte R. Hance4,5,†

  • 1Department of Mathematical Physics, Institute of Physics, University of São Paulo, Rua do Matão 1371, São Paulo 05508-090, São Paulo, Brazil
  • 2Military Institute of Engineering (IME), Defense Engineering Section, Rio de Janeiro, Brazil
  • 3QuIIN–Quantum Industrial Innovation, EMBRAPII CIMATEC Competence Center in Quantum Technologies, SENAI CIMATEC, Av. Orlando Gomes, 1845, Salvador, Bahia 41850-010, Brazil
  • 4School of Computing, Newcastle University, 1 Science Square, Newcastle upon Tyne NE4 5TG, United Kingdom
  • 5Quantum Engineering Technology Laboratories, Department of Electrical and Electronic Engineering, University of Bristol, Woodland Road, Bristol BS8 1US, United Kingdom

  • *Contact author: alisson.tezzin@usp.br
  • †Contact author: jonte.hance@newcastle.ac.uk
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Phys. Rev. A 112, 052208 – Published 10 November, 2025

DOI: https://doi.org/10.1103/65zd-1lys

Abstract

Ontological models, as used in the generalized contextuality literature, play a central role in current research on quantum foundations, providing a framework for defining classicality, constructing classical analogs of key quantum phenomena, and examining the ontology of quantum states. In this work, we show that a counterfactual account of Lüders' rule—which we argue is naturally implied by the mathematical structure of the rule itself—renders such models inherently incompatible with the quantum formalism. This incompatibility arises because the counterfactual update requires ontological models to update their states according to conditional probability, which in turn renders predictions of sequential measurements order-independent. This implies that ontological models, even contextual ones, must either act differently than what we would expect given (this, typically implicitly assumed account of) quantum state update rule, or cannot model quantum behavior.

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Incompatibility of deterministic underlying states with a counterfactual account of Lüders' rule

Alisson Tezzin, Bárbara Amaral, and Jonte R. Hance
Phys. Rev. A 112, L050202 (2025)

Article Text

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Phys. Rev. A 112, 052208– Published 10 November, 2025
  • Received 25 February 2025
  • Revised 19 August 2025
  • Accepted 14 October 2025
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