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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 313, Pages 109–123
DOI: https://doi.org/10.4213/tm4167 (Mi tm4167) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Some Algebraic and Geometric Aspects of Quantum Measurements

A. S. Kocherovaa, I. Yu. Zhdanovskiyab

a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
b Laboratory of Algebraic Geometry and Its Applications, HSE University, ul. Usacheva 6, Moscow, 119048 Russia
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DOI: https://doi.org/10.4213/tm4167
Abstract: We study positive operator-valued measures by algebraic and geometric methods. We prove that positive operator-valued measures are parametrized by a Poisson manifold. Also, we show how to obtain symplectic leaves of this Poisson manifold in terms of parameters of the measures. In addition, we study the interaction of two projection-valued measures by the methods of algebraic geometry.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00908
HSE Basic Research Program
Ministry of Education and Science of the Russian Federation 5-100
The second author was supported in part by the Russian Foundation for Basic Research, project no. 18-01-00908. The work was also supported by the HSE Basic Research Program and the Russian Academic Excellence Project “5-100.”
Received: July 20, 2020
Revised: October 4, 2020
Accepted: November 16, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 313, Pages 99–112
DOI: https://doi.org/10.1134/S0081543821020103
Bibliographic databases:
Document Type: Article
UDC: 512.669.82+530.145.82
Language: Russian
Citation: A. S. Kocherova, I. Yu. Zhdanovskiy, “Some Algebraic and Geometric Aspects of Quantum Measurements”, Mathematics of Quantum Technologies, Collected papers, Trudy Mat. Inst. Steklova, 313, Steklov Math. Inst., Moscow, 2021, 109–123; Proc. Steklov Inst. Math., 313 (2021), 99–112
Citation in format AMSBIB
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\paper Some Algebraic and Geometric Aspects of Quantum Measurements
\inbook Mathematics of Quantum Technologies
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\yr 2021
\vol 313
\pages 109--123
\publ Steklov Math. Inst.
\publaddr Moscow
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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