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  • Letter
  • Open Access

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

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

  • 1Department of Mathematical Physics, Institute of Physics, University of São Paulo, R. do Matão 1371, São Paulo 05508-090, SP, 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, L050202 – Published 10 November, 2025

DOI: https://doi.org/10.1103/mrqr-sdyf

Abstract

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—rules out underlying-state models of quantum mechanics (a type of hidden-variable model, typically used in the contextuality and nonlocality literature, where quantum states are treated as probability measures over “better-defined states”). This incompatibility arises because the counterfactual update requires ontological models to update their states according to conditional probability, which in turn establishes an equivalence between compatibility and the existence of such models.

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

Alisson Tezzin, Bárbara Amaral, and Jonte R. Hance
Phys. Rev. A 112, 052208 (2025)

Article Text

Supplemental Material

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Outline

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Phys. Rev. A 112, L050202– Published 10 November, 2025
  • Received 25 February 2025
  • Revised 19 August 2025
  • Accepted 16 October 2025
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