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

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

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 213–220

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Document Type: Article
UDC: 517.977.5

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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• http://mi.mathnet.ru/eng/tm3623
• https://doi.org/10.1134/S0371968515020132
• http://mi.mathnet.ru/eng/tm/v289/p227

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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
2. D. V. Zhdanov, T. Seideman, “Role of control constraints in quantum optimal control”, Phys. Rev. A, 92 (2015), 052109, arXiv: 1507.08785
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
4. I. V. Volovich, S. V. Kozyrev, “Manipulation of states of a degenerate quantum system”, Proc. Steklov Inst. Math., 294 (2016), 241–251
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
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
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
8. S. V. Kozyrev, “Quantum transport in degenerate systems”, Proc. Steklov Inst. Math., 301 (2018), 134–143
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
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