Artículo
Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden-variable theories
Autor/es | Cabello Quintero, Adán
Portillo Fernández, José Ramón Solís, Alberto Svozil, Karl |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Física Aplicada II |
Fecha de publicación | 2018 |
Fecha de depósito | 2022-07-28 |
Publicado en |
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Resumen | 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 ... 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 |
Agencias financiadoras | Ministerio de Economía y Competitividad (MINECO). España |
Identificador del proyecto | FIS2017-89609-P |
Cita | Cabello Quintero, A., Portillo Fernández, J.R., Solís, A. y Svozil, K. (2018). Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden-variable theories. Physical Review A, 98 (1), 012106-1-012106-8. |
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