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Article: Optimal measurement structures for contextuality applications

TitleOptimal measurement structures for contextuality applications
Authors
Issue Date29-Jun-2023
PublisherNature Research
Citation
npj Quantum Information, 2023, v. 9, n. 1 How to Cite?
Abstract

The Kochen-Specker (KS) theorem is a cornerstone result in the foundations of quantum mechanics describing the fundamental difference between quantum theory and classical non-contextual theories. Recently specific substructures termed 01-gadgets were shown to exist within KS proofs that capture the essential contradiction of the theorem. Here, we show these gadgets and their generalizations provide an optimal toolbox for contextuality applications including (i) constructing classical channels exhibiting entanglement-assisted advantage in zero-error communication, (ii) identifying large separations between quantum theory and binary generalized probabilistic theories, and (iii) finding optimal tests for contextuality-based semi-device-independent randomness generation. Furthermore, we introduce and study a generalization to definite prediction sets for more general logical propositions, that we term higher-order gadgets. We pinpoint the role these higher-order gadgets play in KS proofs by identifying these as induced subgraphs within KS graphs and showing how to construct proofs of state-independent contextuality using higher-order gadgets as building blocks. The constructions developed here may help in solving some of the remaining open problems regarding minimal proofs of the Kochen-Specker theorem.


Persistent Identifierhttp://hdl.handle.net/10722/338729
ISSN
2023 Impact Factor: 6.6
2023 SCImago Journal Rankings: 2.824
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLiu, Yuan-
dc.contributor.authorRamanathan, Ravishankar-
dc.contributor.authorHorodecki, Karol-
dc.contributor.authorRosicka, Monika-
dc.contributor.authorHorodecki, Paweł-
dc.date.accessioned2024-03-11T10:31:06Z-
dc.date.available2024-03-11T10:31:06Z-
dc.date.issued2023-06-29-
dc.identifier.citationnpj Quantum Information, 2023, v. 9, n. 1-
dc.identifier.issn2056-6387-
dc.identifier.urihttp://hdl.handle.net/10722/338729-
dc.description.abstract<p>The Kochen-Specker (KS) theorem is a cornerstone result in the foundations of quantum mechanics describing the fundamental difference between quantum theory and classical non-contextual theories. Recently specific substructures termed 01-gadgets were shown to exist within KS proofs that capture the essential contradiction of the theorem. Here, we show these gadgets and their generalizations provide an optimal toolbox for contextuality applications including (i) constructing classical channels exhibiting entanglement-assisted advantage in zero-error communication, (ii) identifying large separations between quantum theory and binary generalized probabilistic theories, and (iii) finding optimal tests for contextuality-based semi-device-independent randomness generation. Furthermore, we introduce and study a generalization to definite prediction sets for more general logical propositions, that we term higher-order gadgets. We pinpoint the role these higher-order gadgets play in KS proofs by identifying these as induced subgraphs within KS graphs and showing how to construct proofs of state-independent contextuality using higher-order gadgets as building blocks. The constructions developed here may help in solving some of the remaining open problems regarding minimal proofs of the Kochen-Specker theorem.<br></p>-
dc.languageeng-
dc.publisherNature Research-
dc.relation.ispartofnpj Quantum Information-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.titleOptimal measurement structures for contextuality applications-
dc.typeArticle-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1038/s41534-023-00728-2-
dc.identifier.scopuseid_2-s2.0-85163726487-
dc.identifier.volume9-
dc.identifier.issue1-
dc.identifier.eissn2056-6387-
dc.identifier.isiWOS:001021227000001-
dc.identifier.issnl2056-6387-

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