Artículo
Bell non-locality and Kochen-Specker contextuality: how are they connected?
Autor/es | Cabello Quintero, Adán |
Departamento | Universidad de Sevilla. Departamento de Física Aplicada II |
Fecha de publicación | 2021-05-22 |
Fecha de depósito | 2022-07-18 |
Publicado en |
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Resumen | Bell non-locality and Kochen–Specker (KS) contextuality are logically independent concepts, fuel different protocols with quantum vs classical advantage, and have distinct classical simulation costs. A natural question is ... Bell non-locality and Kochen–Specker (KS) contextuality are logically independent concepts, fuel different protocols with quantum vs classical advantage, and have distinct classical simulation costs. A natural question is what are the relations between these concepts, advantages, and costs. To address this question, it is useful to have a map that captures all the connections between Bell non-locality and KS contextuality in quantum theory. The aim of this work is to introduce such a map. After defining the theory-independent notions of Bell non-locality and KS contextuality for ideal measurements, we show that, in quantum theory, due to Neumark’s dilation theorem, every quantum Bell non-local behavior can be mapped to a formally identical KS contextual behavior produced in a scenario with identical relations of compatibility but where measurements are ideal and no space-like separation is required. A more difficult problem is identifying connections in the opposite direction. We show that there are “one-to-one” and partial connections between KS contextual behaviors and Bell non-local behaviors for some KS scenarios, but not for all of them. However, there is also a method that transforms any KS contextual behavior for quantum systems of dimension d into a Bell non-local behavior between two quantum subsystems each of them of dimension d. We collect all these connections in map and list some problems which can benefit from this map. |
Agencias financiadoras | Universidad de Sevilla European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Ministerio de Economia, Industria y Competitividad (MINECO). España |
Identificador del proyecto | US-15097
FIS2017-89609-P PCI2019-111885-2 |
Cita | Cabello Quintero, A. (2021). Bell non-locality and Kochen-Specker contextuality: how are they connected?. Foundations of Physics, 51(61) |
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