Bell Inequalities with One Bit of Communication

Bell Inequalities with One Bit of Communication

We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We developed a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult. Using this method, we partially solved the scenario where Al...

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Bibliographic Details
Main Authors: Emmanuel Zambrini Cruzeiro, Nicolas Gisin
Format: Article
Language:English
Published: MDPI AG 2019-02-01
Series:Entropy
Subjects:
quantum nonlocality
communication complexity
Online Access:https://www.mdpi.com/1099-4300/21/2/171
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spelling doaj-326ef642edad41608cbf216b466939842020-11-24T20:40:18ZengMDPI AGEntropy1099-43002019-02-0121217110.3390/e21020171e21020171Bell Inequalities with One Bit of CommunicationEmmanuel Zambrini Cruzeiro0Nicolas Gisin1Department of Applied Physics, University of Geneva, 1211 Geneva, SwitzerlandDepartment of Applied Physics, University of Geneva, 1211 Geneva, SwitzerlandWe study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We developed a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult. Using this method, we partially solved the scenario where Alice and Bob choose between three inputs, finding a total of 668 inequivalent facet inequalities (with respect to relabelings of inputs and outputs). We also show that some of these inequalities are constructed from facet inequalities found in scenarios without communication, that is, the well-known Bell inequalities.https://www.mdpi.com/1099-4300/21/2/171quantum nonlocalitycommunication complexity
collection DOAJ
language English
format Article
sources DOAJ
author Emmanuel Zambrini Cruzeiro
Nicolas Gisin
spellingShingle Emmanuel Zambrini Cruzeiro
Nicolas Gisin
Bell Inequalities with One Bit of Communication
Entropy
quantum nonlocality
communication complexity
author_facet Emmanuel Zambrini Cruzeiro
Nicolas Gisin
author_sort Emmanuel Zambrini Cruzeiro
title Bell Inequalities with One Bit of Communication
title_short Bell Inequalities with One Bit of Communication
title_full Bell Inequalities with One Bit of Communication
title_fullStr Bell Inequalities with One Bit of Communication
title_full_unstemmed Bell Inequalities with One Bit of Communication
title_sort bell inequalities with one bit of communication
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2019-02-01
description We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We developed a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult. Using this method, we partially solved the scenario where Alice and Bob choose between three inputs, finding a total of 668 inequivalent facet inequalities (with respect to relabelings of inputs and outputs). We also show that some of these inequalities are constructed from facet inequalities found in scenarios without communication, that is, the well-known Bell inequalities.
topic quantum nonlocality
communication complexity
url https://www.mdpi.com/1099-4300/21/2/171
work_keys_str_mv AT emmanuelzambrinicruzeiro bellinequalitieswithonebitofcommunication
AT nicolasgisin bellinequalitieswithonebitofcommunication
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