A Classification of Hidden-Variable Properties
arXiv:0711.4650 · doi:10.1088/1751-8113/41/42/425302
Abstract
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present six such properties and a Venn diagram of how they are related. With two existence theorems and three no-go theorems (EPR, Bell, and Kochen-Specker), we show which properties of empirically equivalent hidden-variable models are possible and which are not. Formally, our treatment relies only on classical probability models, and physical phenomena are used only to motivate which models to choose.
28 pages; added references; clearer exposition. Final version
References in corpus (7)
- Hidden Variables and the Two Theorems of John Bell
- The Free Will Theorem
- Bell-Kochen-Specker theorem: A proof with 18 vectors
- Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
- A local hidden variable theory for the GHZ experiment
- Locality and Causality in Hidden Variables Models of Quantum Theory
- EPR and Bell Locality
Cited by in corpus (20)
- The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
- Beyond Bell's Theorem: Correlation Scenarios
- Proposal for a quantum delayed-choice experiment
- Relational Hidden Variables and Non-Locality
- Is wave-particle objectivity compatible with determinism and locality?
- Experimental entanglement-assisted quantum delayed-choice experiment
- Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality
- Quantum control in foundational experiments
- A Rigorous Analysis of the Clauser-Horne-Shimony-Holt Inequality Experiment When Trials Need Not Be Independent
- Determinism, independence and objectivity are incompatible
- Nonlocality with less Complementarity
- Quantum realism and quantum surrealism
- Controlling wave-particle duality with quantum entanglement
- Continuous-variable nonlocality and contextuality
- Spooky action at a distance in general probabilistic theories
- Wigner and friends, a map is not the territory! Contextuality in multi-agent paradoxes
- Reflections on the PBR Theorem: Reality Criteria & Preparation Independence
- The Interplay between Quantum Contextuality and Wigner Negativity
- Uncertainty principle certifies genuine source of intrinsic randomness
- Differential Geometry of Contextuality