Birkhoff–von Neumann's theorem, doubly normalized tensors, and joint measurability

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MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.contributorCentro de Ciências Naturais e Exatas–Universidade Federal de Santa Maria-
Autor(es): dc.contributorInstituto de Matemática e Estatística–Universidade Federal do Rio Grande do Sul-
Autor(es): dc.creatorGuerini, Leonardo-
Autor(es): dc.creatorBaraviera, Alexandre-
Data de aceite: dc.date.accessioned2025-08-21T22:37:11Z-
Data de disponibilização: dc.date.available2025-08-21T22:37:11Z-
Data de envio: dc.date.issued2023-07-29-
Data de envio: dc.date.issued2023-07-29-
Data de envio: dc.date.issued2021-12-31-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.1080/03081087.2022.2158164-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/248123-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/248123-
Descrição: dc.descriptionQuantum measurements can be interpreted as a generalization of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalization of doubly stochastic matrices that we call doubly normalized tensors (DNTs), and investigate a corresponding version of Birkhoff–von Neumann's theorem, which states that permutations are the extremal points of the set of doubly stochastic matrices. We prove that joint measurability appears naturally as a mathematical feature of DNTs in this context and that this feature is necessary and sufficient for a characterization similar to Birkhoff–von Neumann's. Conversely, we also show that DNTs arise from a particular instance of a joint measurability problem, remarking the relevance of this quantum-theoretical property in general operator theory.-
Descrição: dc.descriptionInternational Centre for Theoretical Physics – South American Institute for Fundamental Research & Instituto de Física Teórica – UNESP-
Descrição: dc.descriptionCentro de Ciências Naturais e Exatas–Universidade Federal de Santa Maria-
Descrição: dc.descriptionInstituto de Matemática e Estatística–Universidade Federal do Rio Grande do Sul-
Descrição: dc.descriptionInternational Centre for Theoretical Physics – South American Institute for Fundamental Research & Instituto de Física Teórica – UNESP-
Idioma: dc.languageen-
Relação: dc.relationLinear and Multilinear Algebra-
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Título: dc.titleBirkhoff–von Neumann's theorem, doubly normalized tensors, and joint measurability-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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