title: On extension of the family of projections to positive operator-valued measure
metadata.name: dc.contributor.author
metadata.value: Alekseev, Anton O.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Amosov, Grigori G.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-03-14T19:05:05Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-03-14T19:05:05Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Alekseev A.O., Amosov G.G. On extension of the family of projections to positive operator-valued measure. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 1, pp. 3–13. https://doi.org/10.21638/spbu01.2023.101 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.101
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/39321
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of constructing a measure on a discrete set X taking values in a positive cone of bounded operators in a Hilbert space is considered. It is assumed that a projectionvalued function defined on a subset of X0 of the original set X is initially given. The aim of the study is to find such a scalar measure μ on the set X and the continuation of a projector-valued function from X0 to X, which results in an operator-valued measure having a projector-valued density relative to μ. In general, the problem is solved for |X| = 4 and |X0| = 2. As an example, we consider a function on X0 that takes values in a set of projections on coherent states. For this case, the question of the information completeness of the measurement determined by the constructed measure is investigated. In other words, is it possible to reconstruct a quantum state (a positive unit trace operator) from the values of the matrix trace from the product of a measure with a quantum state. It is shown that for the constructed measure it is possible to restore the quantum state only if it is a projection. A restriction on the probability distribution is also found, at which it can be obtained as a result of measuring a certain quantum state.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Russian Science Foundation grant no. 19-11-00086,
  https://rscf.ru/en/project/19-11-00086/.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 10 (68); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: operator-valued measure
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: coherent states
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: informational completeness
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On extension of the family of projections to positive operator-valued measure
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15489-Текст статьи-51840-1-2-20230304.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/39321/1/15489-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-51840-1-2-20230304.pdf
resources.format: Adobe PDF
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