Critical point in the problem of maximizing the transition probability using measurements in an $n$-level quantum system
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 3, pp. 445-451 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of maximizing the transition probability in an $n$-level quantum system from a given initial state to a given final state using nonselective quantum measurements. We find a sequence of measurements that is a critical point of the transition probability and, moreover, a local maximum in each variable on the set of one-dimensional projectors. We consider the class of one-dimensional projectors because these projectors describe the measurements of populations of pure states of the system.
Keywords: multilevel quantum system, open quantum system, quantum measurement, quantum system control.
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N. B. Il'in; A. N. Pechen'. Critical point in the problem of maximizing the transition probability using measurements in an $n$-level quantum system. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 3, pp. 445-451. http://geodesic.mathdoc.fr/item/TMF_2018_194_3_a5/

[1] S. A. Rice, M. Zhao, Optical Control of Molecular Dynamics, Wiley, New York, 2000

[2] M. Shapiro, P. W. Brumer, Principles of the Quantum Control of Molecular Processes, Wiley, Hobooken, 2003

[3] D. J. Tannor, Introduction to Quantum Mechanics: A Time Dependent Perspective, Univ. Sci. Books, Sausalito, CA, 2007

[4] D. D'Alessandro, Introduction to Quantum Control and Dynamics, Chapman Hall, Boca Raton, FL, 2008 | MR | Zbl

[5] V. S. Letokhov, Laser Control of Atoms and Molecules, Oxford Univ. Press, New York, 2007

[6] C. Brif, R. Chakrabarti, H. Rabitz, “Control of quantum phenomena”, Adv. Chem. Phys., 148 (2012), 1–76 | DOI

[7] S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen, D. Sugny, F. K. Wilhelm, “Training Schrödinger's cat: quantum optimal control”, Eur. Phys. J. D, 69 (2015), 279, 24 pp. | DOI

[8] L. Accardi, S. V. Kozyrev, A. N. Pechen, “Coherent quantum control of $\Lambda$-atoms through the stochastic limit”, Quantum Information and Computing, $QP$–$PQ$: Quantum Probability and White Noise Analysis, 19, eds. L. Accardi, M. Ohya, N. Watanabe, World Sci., Singapore, 2006, 1–17 | Zbl

[9] A. I. Zenchuk, S. I. Doronin, “Udalennyi kontrol kvantovymi korrelyatsiyami dvukhkubitnogo priemnika posredstvom trekhkubitnogo peredatchika”, TMF, 188:2 (2016), 343–358 | DOI | DOI | MR

[10] K. A. Lyakhov, H. J. Lee, A. N. Pechen, “Some features of Boron isotopes separation by the laser-assisted retardation of condensation method in multipass irradiation cell implemented as a resonator”, IEEE J. Quantum Electron., 52:12 (2016), 1400208, 8 pp. | DOI

[11] S. V. Kozyrev, A. A. Mironov, A. E. Teretenkov, I. V. Volovich, “Flows in nonequilibrium quantum systems and quantum photosynthesis”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4 (2017), 1750021 | DOI

[12] A. S. Holevo, Statistical Structure of Quantum Theory, Lecture Notes in Physics. Monographs, 67, Springer, Berlin, 2001 | DOI | MR

[13] M. Ohya, I. Volovich, Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-Systems, Springer, Dordrecht, 2011 | DOI | MR

[14] I. V. Volovich, S. V. Kozyrev, “Manipulyatsiya sostoyaniyami vyrozhdennoi kvantovoi sistemy”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Tr. MIAN, 294, 2016, 256–267 | DOI | MR | Zbl

[15] 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, 16 pp., arXiv: 1607.07572 | DOI | MR | Zbl

[16] A. N. Pechen, N. B. Ilin, F. Shuang, H. Rabitz, “Quantum control by von Neumann measurements”, Phys. Rev. A, 74:5 (2006), 052102, 7 pp. | DOI

[17] H. W. Wiseman, “Quantum control: squinting at quantum systems”, Nature, 470 (2011), 178–179 | DOI

[18] J. Gough, V. P. Belavkin, O. G. Smolyanov, “Hamilton–Jacobi–Bellman equations for quantum optimal feedback control”, J. Opt. B: Quantum Semiclass. Opt., 7:10 (2005), S237–S244 | DOI | MR

[19] R. Vilela Mendes, V. I. Man'ko, “Quantum control and the Strocchi map”, Phys. Rev. A, 67:5 (2003), 053404, 8 pp. | DOI

[20] B. Misra, E. C. G. Sudarshan, “The Zeno's paradox in quantum theory”, J. Math. Phys., 18:4 (1977), 756–763 | DOI | MR

[21] A. P. Balachandran, S. M. Roy, “Quantum anti-Zeno paradox”, Phys. Rev. Lett., 84:18 (2000), 4019–4022 | DOI | MR

[22] F. Shuang, A. N. Pechen, T. S. Ho, H. Rabitz, “Observation–assisted optimal control of quantum dynamics”, J. Chem. Phys., 126:13 (2007), 134303, 7 pp. | DOI

[23] M. S. Blok, C. Bonato, M. L. Markham, D. J. Twitchen, V. V. Dobrovitski, R. Hanson, “Manipulating a qubit through the backaction of sequential partial measurements and real–time feedback”, Nature Phys., 10 (2014), 189–193 | DOI

[24] G. A. Paz-Silva, A. T. Rezakhani, J. M. Dominy, D. A. Lidar, “Zeno effect for quantum computation and control”, Phys. Rev. Lett., 108:8 (2012), 080501, 5 pp. | DOI

[25] A. N. Pechen, A. S. Trushechkin, “Measurement-assisted Landau–Zener transitions”, Phys. Rev. A, 91:5 (2015), 052316, 15 pp. | DOI

[26] M. G. Ivanov, “O edinstvennosti kvantovoi teorii izmerenii dlya tochnykh izmerenii s diskretnym spektrom”, Tr. MFTI, 8:1(29) (2016), 170–178

[27] M. B. Menskii, “Evolyutsiya kvantovoi sistemy, podvergayuscheisya nepreryvnomu izmereniyu”, TMF, 75:1 (1988), 41–52 | DOI | MR

[28] M. Campisi, P. Talkner, P. Hanngi, “Influence of measurements on the statistics of work performed on a quantum system”, Phys. Rev. E, 83:4 (2011), 041114, 7 pp. | DOI

[29] A. Hentschel, B. C. Sanders, “Machine learning for precise quantum measurement”, Phys. Rev. Lett., 104:6 (2010), 063603, 4 pp. | DOI

[30] H. Rabitz, H. Hsieh, C. Rosenthal, “Quantum optimally controlled transition landscapes”, Science, 303:5666 (2004), 1998–2001 | DOI

[31] T. S. Ho, H. Rabitz, “Why do effective quantum controls appear easy to find?”, J. Photochem. Photobiol. A, 180:3 (2006), 226–240 | DOI

[32] P. de Fouquieres, S. G. Schirmer, “A closer look at quantum control landscapes and their implication for control optimization”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 16:3 (2013), 1350021, 24 pp. | MR | Zbl

[33] N. Rach, M. M. Müller, T. Calarco, S. Montangero, “Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape”, Phys. Rev. A, 92:6 (2015), 062343, 7 pp. | DOI

[34] A. N. Pechen, N. B. Ilin, “O kriticheskikh tochkakh tselevogo funktsionala v zadache maksimizatsii nablyudaemykh kubita”, UMN, 70:4(424) (2015), 211–212 | DOI | DOI | MR | Zbl

[35] A. N. Pechen, “O metode skorostnogo gradienta dlya generatsii unitarnykh kvantovykh operatsii v zamknutykh kvantovykh sistemakh”, UMN, 71:3(429) (2016), 205–206 | DOI | MR | Zbl

[36] A. N. Pechen, N. B. Il'in, “Control landscape for ultrafast manipulation by a qubit”, J. Phys. A: Math. Theor., 50:7 (2017), 075301, 13 pp. | DOI | MR | Zbl

[37] A. N. Pechen, N. B. Ilin, “O zadache maksimizatsii veroyatnosti perekhoda v $n$-urovnevoi kvantovoi sisteme s pomoschyu neselektivnykh izmerenii”, Tr. MIAN, 294 (2016), 248–255 | DOI | DOI | MR