Typing Quantum Superpositions and Measurement

We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-type...

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Detalles Bibliográficos
Autores: Díaz Caro, Alejandro, Dowek, Gilles
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/42228
Acceso en línea:http://hdl.handle.net/11336/42228
Access Level:acceso abierto
Palabra clave:QUANTUM COMPUTING
LAMBDA CALCULUS
ALGEBRAIC LINEARITY
LINEAR LOGIC
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
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repository_id_str
spelling Typing Quantum Superpositions and MeasurementDíaz Caro, AlejandroDowek, GillesQUANTUM COMPUTINGLAMBDA CALCULUSALGEBRAIC LINEARITYLINEAR LOGIChttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.Fil: Díaz Caro, Alejandro. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dowek, Gilles. Institut National de Recherche en Informatique et en Automatique; FranciaSpringer2017-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/42228Díaz Caro, Alejandro; Dowek, Gilles; Typing Quantum Superpositions and Measurement; Springer; Lecture Notes in Computer Science; 10687; 12-2017; 281-293978-3-319-71069-30302-9743CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/978-3-319-71069-3_22info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-71069-3_22info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:06:34Zoai:ri.conicet.gov.ar:11336/42228instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982024-05-08 14:06:34.758CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Typing Quantum Superpositions and Measurement
title Typing Quantum Superpositions and Measurement
spellingShingle Typing Quantum Superpositions and Measurement
Díaz Caro, Alejandro
QUANTUM COMPUTING
LAMBDA CALCULUS
ALGEBRAIC LINEARITY
LINEAR LOGIC
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
title_short Typing Quantum Superpositions and Measurement
title_full Typing Quantum Superpositions and Measurement
title_fullStr Typing Quantum Superpositions and Measurement
title_full_unstemmed Typing Quantum Superpositions and Measurement
title_sort Typing Quantum Superpositions and Measurement
dc.creator.none.fl_str_mv Díaz Caro, Alejandro
Dowek, Gilles
author Díaz Caro, Alejandro
author_facet Díaz Caro, Alejandro
Dowek, Gilles
author_role author
author2 Dowek, Gilles
author2_role author
dc.subject.none.fl_str_mv QUANTUM COMPUTING
LAMBDA CALCULUS
ALGEBRAIC LINEARITY
LINEAR LOGIC
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
topic QUANTUM COMPUTING
LAMBDA CALCULUS
ALGEBRAIC LINEARITY
LINEAR LOGIC
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
description We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/42228
Díaz Caro, Alejandro; Dowek, Gilles; Typing Quantum Superpositions and Measurement; Springer; Lecture Notes in Computer Science; 10687; 12-2017; 281-293
978-3-319-71069-3
0302-9743
CONICET Digital
CONICET
url http://hdl.handle.net/11336/42228
identifier_str_mv Díaz Caro, Alejandro; Dowek, Gilles; Typing Quantum Superpositions and Measurement; Springer; Lecture Notes in Computer Science; 10687; 12-2017; 281-293
978-3-319-71069-3
0302-9743
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/978-3-319-71069-3_22
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-71069-3_22
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 15.812429

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