Deterministic Underlying States are incompatible with a Counterfactual account of Lüders' rule
arXiv:2502.00546 · doi:10.1103/mrqr-sdyf
Abstract
In this work, we show that a counterfactual account of L"uders' 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.
4+3 pages, no figures. Accepted for publication by Phys. Rev. A as a Letter. Matches accepted version
References in corpus (12)
- Bell nonlocality
- In defense of the epistemic view of quantum states: a toy theory
- Contextuality for preparations, transformations, and unsharp measurements
- The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
- Graph-Theoretic Approach to Quantum Correlations
- Kochen-Specker Contextuality
- Kochen-Specker theorem for von Neumann algebras
- All quantum observables in a hidden-variables model must commute simultaneously
- Experimental test of contextuality in quantum and classical systems
- Counterfactual restrictions and Bell's theorem
- Efficient contextual ontological model of -qubit stabilizer quantum mechanics
- Sufficiency of the counterfactual account of Lüders' rule to rule out ontological models of quantum mechanics