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Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 3, Pages 62–67 (Mi ivm8784)  

This article is cited in 2 scientific papers (total in 2 papers)

Brief communications

Reconstruction of a pure state from incomplete information on its optical tomogram

G. G. Amosova, A. I. Dnestryanb

a Department of Probability and Statistics, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Chair of Higher Mathematics, Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow, Russia

Abstract: We consider the problem of reconstructing a state (i.e., a positive unit-trace operator) from incomplete information on its optical tomogram. In the case, when a (pure) state is determined by a function representing a linear combination of $N$ ground and excited states of a quantum oscillator, we propose a technique for reconstructing this state from $N$ values of its tomogram. For $N=3$ we find an exact solution to the problem under consideration.

Keywords: state, optical tomogram, eigenfunctions of integral operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-02-00312-a
11-02-00456-a
12-01-00319-a
Russian Academy of Sciences - Federal Agency for Scientific Organizations


Full text: PDF file (171 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:3, 51–55

UDC: 517.98
Presented by the member of Editorial Board: А. М. Бикчентаев
Received: 07.08.2012

Citation: G. G. Amosov, A. I. Dnestryan, “Reconstruction of a pure state from incomplete information on its optical tomogram”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 3, 62–67; Russian Math. (Iz. VUZ), 57:3 (2013), 51–55

Citation in format AMSBIB
\Bibitem{AmoDne13}
\by G.~G.~Amosov, A.~I.~Dnestryan
\paper Reconstruction of a~pure state from incomplete information on its optical tomogram
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 3
\pages 62--67
\mathnet{http://mi.mathnet.ru/ivm8784}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 3
\pages 51--55
\crossref{https://doi.org/10.3103/S1066369X13030079}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84876231479}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Amosov G.G., Dnestryan A.I., “Towards a Tomographic Representation of Quantum Mechanics on the Plane”, Phys. Scr., 90:7, SI (2015), 074025  crossref  isi  elib
    2. A. I. Dnestryan, “Ob opredelenii chistykh sostoyanii metodom gomodinnogo detektirovaniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:1 (2016), 33–42  mathnet  crossref  zmath  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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