Least-bias state estimation with incomplete unbiased measurements

Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing unbiasedness on the probabilities for the unmeasured bases does not...

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Detalhes bibliográficos
Autores: Řeháček, Jaroslav, Hradil, Zdenek, Teo, Yong Siah, Sánchez Soto, Luis Lorenzo, Ng, Hui Khoon, Chai, Jing Hao, Englert, Berthold-Georg
Formato: artículo
Fecha de publicación:2015
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/24289
Acesso em linha:https://hdl.handle.net/20.500.14352/24289
Access Level:acceso abierto
Palavra-chave:535
Informationally complete measurements
Statistical-mechanics
Quantum tomography
Bases
Dimensions
System
Óptica (Física)
2209.19 Óptica Física
Descrição
Resumo:Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing unbiasedness on the probabilities for the unmeasured bases does not generally yield the estimator with the largest von Neumann entropy, a popular figure of merit in this context. Furthermore, this imposition typically leads to mock density matrices that are not even positive definite. This provides a strong argument against perfunctory applications of linear estimation strategies. We propose to use instead the physical state estimators that maximize the Shannon entropy of the unmeasured outcomes, which quantifies our lack of knowledge fittingly and gives physically meaningful statistical predictions.