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Tr. Mat. Inst. Steklova, 2015, Volume 289, Pages 227–234 (Mi tm3623)  

This article is cited in 9 scientific papers (total in 9 papers)

Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times

A. N. Pechen, N. B. Il'in

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We consider the Mayer maximization problem for an objective functional that describes the average value at some fixed time of a quantum-mechanical observable for a two-level quantum system (qubit). In the previous studies we proved that for sufficiently large times the objective functional has no local maxima that are not global maxima. Such local maxima that are not global are called traps. In this paper we prove that for sufficiently short times under certain conditions traps for this problem do exist.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515020132

Full text: PDF file (186 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 213–220

Bibliographic databases:

Document Type: Article
UDC: 517.977.5
Received: February 15, 2015

Citation: A. N. Pechen, N. B. Il'in, “Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Tr. Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 227–234; Proc. Steklov Inst. Math., 289 (2015), 213–220

Citation in format AMSBIB
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\paper Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 227--234
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968515020132}
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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. A. N. Pechen, N. B. Il'in, “On critical points of the objective functional for maximization of qubit observables”, Russian Math. Surveys, 70:4 (2015), 782–784  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. D. V. Zhdanov, T. Seideman, “Role of control constraints in quantum optimal control”, Phys. Rev. A, 92 (2015), 052109, arXiv: 1507.08785  crossref  adsnasa  isi  scopus
    3. Alexander N. Pechen, Nikolay B. Il'in, “On the problem of maximizing the transition probability in an $n$-level quantum system using nonselective measurements”, Proc. Steklov Inst. Math., 294 (2016), 233–240  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. I. V. Volovich, S. V. Kozyrev, “Manipulation of states of a degenerate quantum system”, Proc. Steklov Inst. Math., 294 (2016), 241–251  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. A. N. Pechen, N. B. Il'in, “Control landscape for ultrafast manipulation by a qubit”, J. Phys. A-Math. Theor., 50:7 (2017), 075301  crossref  mathscinet  zmath  isi  scopus
    6. S. V. Kozyrev, A. A. Mironov, A. E. Teretenkov, I. V. Volovich, “Flows in non-equilibrium quantum systems and quantum photosynthesis”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4 (2017), 1750021  crossref  mathscinet  zmath  isi  scopus
    7. A. Trushechkin, “Semiclassical evolution of quantum wave packets on the torus beyond the Ehrenfest time in terms of Husimi distributions”, J. Math. Phys., 58:6 (2017), 062102  crossref  mathscinet  zmath  isi  scopus
    8. S. V. Kozyrev, “Quantum transport in degenerate systems”, Proc. Steklov Inst. Math., 301 (2018), 134–143  mathnet  crossref  crossref  isi  elib  elib
    9. A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271  mathnet  crossref  crossref  isi  elib  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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