Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden-variable theories
An essential ingredient in many examples of the conflict between quantum theory and noncontextual hidden variables (e.g., the proof of the Kochen-Specker theorem and Hardy’s proof of Bell’s theorem) is a set of atomic propositions about the outcomes of ideal measurements such that, when outcome nonc...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/135950 |
| Acceso en línea: | https://hdl.handle.net/11441/135950 https://doi.org/10.1103/PhysRevA.98.012106 |
| Access Level: | acceso abierto |
| Sumario: | An essential ingredient in many examples of the conflict between quantum theory and noncontextual hidden variables (e.g., the proof of the Kochen-Specker theorem and Hardy’s proof of Bell’s theorem) is a set of atomic propositions about the outcomes of ideal measurements such that, when outcome noncontextuality is assumed, if proposition A is true, then, due to exclusiveness and completeness, a nonexclusive proposition B (C) must be false (true). We call such a set a true-implies-false set (TIFS) [true-implies-true set (TITS)]. Here we identify all the minimal TIFSs and TITSs in every dimension d 3, i.e., the sets of each type having the smallest number of propositions. These sets are important because each of them leads to a proof of impossibility of noncontextual hidden variables and correspondsto a simple situation with quantumvs classical advantage.Moreover, themethods developed to identify them may be helpful to solve some open problems regarding minimal Kochen-Specker sets |
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