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

Autor(es)

Guerini, Leonardo ; Baraviera, Alexandre

• Tipo de documento: Artigo Científico
• Fonte: LINEAR & MULTILINEAR ALGEBRA; v. N/A, p. 14-pg., 2022-12-29.

Resumo

Quantum 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. (AU)

• Processo FAPESP: 18/04208-9 - Simulabilidade da medida quântica e aplicações a não-localidade de Bell
• Beneficiário: Leonardo Guerini de Souza
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 16/01343-7 - ICTP Instituto Sul-Americano para Física Fundamental: um centro regional para física teórica
• Beneficiário: Nathan Jacob Berkovits
• Modalidade de apoio: Auxílio à Pesquisa - Projetos Especiais