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119991, Russia
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Laboratory of Mathematical Methods of Quantum Technologies

| Areas of Research | Publications |
Staff
Pechen Alexander Nikolaevich

Doctor Phys.-Math. Sci., Professor of RAS, Head of Laboratory
office: 434; tel.: +7 (495) 984 81 41 * 39 34; e-mail: pechen@mi.ras.ru
Principal fields of research: Dynamics of open quantum systems. Quantum control.
Pechen Alexander Nikolaevich
Kiktenko Evgeniy Olegovich

Scientific Researcher
e-mail: evgeniy.kiktenko@gmail.com
Kiktenko Evgeniy Olegovich
Kronberg Dmitry Anatolievich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
e-mail: dmitry.kronberg@gmail.com
Kronberg Dmitry Anatolievich
Lychkovskiy Oleg Valentinovich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
e-mail: lychkovskiy@mi.ras.ru
Lychkovskiy Oleg Valentinovich
Top
Areas of Research
The Laboratory of Mathematical Methods of Quantum Technologies was established in 2016 with the goal of solving mathematical problems necessary for the development of quantum technologies. The basis of quantum technologies is the use of specific properties of individual quantum systems such as photons, atoms, molecules. These properties include superposition of quantum states, quantum entanglement, the Heisenberg uncertainty principle, and other. Quantum technologies develop in such directions as quantum computers, quantum cryptography, quantum metrology, quantum sensors, etc. In this area, a number of mathematical problems arise, which are investigated by the employees of the laboratory. In particular, the laboratory conducts research in the following areas:
  • Control of quantum systems;
  • Dynamics of open quantum systems;
  • Quantum cryptography;
  • Quantum teleportation.
Employees of the laboratory together with colleagues from the Department of Mathematical Physics and the Russian Quantum Center read in the Steklov Institute the course of lectures Quantum Cryptography.
Recent publications

| by years | scientific publications | by types |



   2017
1. Alexander Pechen, Nikolay Il'in, “Control landscape for ultrafast manipulation by a qubit”, J. Phys. A, 50:7 (2017), 75301 , 14 pp.  mathnet  crossref  isi  scopus
2. K.A. Lyakhov, H.J. Lee, A.N. Pechen, “Some issues of industrial scale boron isotopes separation by the laser assisted retarded condensation (SILARC) method”, Sep. Purif. Technol., 176:4 (2017), 402–411  mathnet  crossref  isi  scopus
3. A. N. Pechen, “Some mathematical problems of control of quantum systems”, Quantum computing, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 76–81  mathnet
4. N. B. Il'in, A. N. Pechen, “Discrete approximations of dynamical quantum Zeno effect”, Quantum computing, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 50–59  mathnet
5. N. Il'in, E. Shpagina, F. Uskov, O. Lychkovskiy, Squaring parametrization of constrained and unconstrained sets of quantum states, 2017 , arXiv: 1704.03861
6. D. A. Kronberg, E. O. Kiktenko, A. K. Fedorov, Yu. V. Kurochkin, “Analysis of coherent quantum cryptography protocol vulnerability to an active beam-splitting attack”, Quantrum Electron., 47:2 (2017), 163–168  mathnet  crossref  isi  elib  scopus
7. D. A. Kronberg, “New methods of error correction in quantum cryptography using low-density parity-check codes”, Matem. vopr. kriptogr., 8:2 (2017), 77–86  mathnet  elib
8. A. S. Trushechkin, P. A. Tregubov, E. O. Kiktenko, Y. V. Kurochkin, A. K. Fedorov, Quantum key distribution protocol with pseudorandom bases, 2017 , 16 pp., arXiv: 1706.00611
9. E. O. Kiktenko, N. O. Pozhar, M. N. Anufriev, A. S. Trushechkin, R. R. Yunusov, Y. V. Kurochkin, A. I. Lvovsky, A. K. Fedorov, Quantum-secured blockchain, 2017 , 8 pp., arXiv: 1705.09258
10. E. O. Kiktenko, N. O. Pozhar, A. V. Duplinskiy, A. A. Kanapin, A. S. Sokolov, S. S. Vorobey, A. V. Miller, V. E. Ustimchik, M. N. Anufriev, A. S. Trushechkin, R. R. Yunusov, V. L. Kurochkin, Y. V. Kurochkin, A. K. Fedorov, Demonstration of a quantum key distribution network across urban fiber channels, 2017 , 5 pp., arXiv: 1705.07154
11. E. O. Kiktenko, A. S. Trushechkin, A. K. Fedorov, Symmetric blind information reconciliation and hash-function-based verification for quantum key distribution, 2017 , 4 pp., arXiv: 1705.06664
12. E. O. Kiktenko, “Study of probable and quasi-probable distributions with the help of specialized software”, Meždunar. nauč.-issled. žurn., 2017, no. 6(60), 72–81  mathnet  crossref  elib
13. A. S. Trushechkin, E. O. Kiktenko, A. K. Fedorov, “Practical issues in decoy-state quantum key distribution based on the central limit theorem”, Phys. Rev. A, 96:2 (2017) , 7 pp., arXiv: 1702.08531  mathnet  crossref  isi

   2016
14. Valentina Markusova, Konstantin Fursov, Aleksandr Pechen, Natalya Ivanova, Sergei Dmitriev, Artëm Oganov i dr., “Kak ukrepit pozitsii rossiiskoi nauki v mire? Itogi onlain-diskussii po voprosam publikatsionnoi aktivnosti”, Elektronnoe izdanie NAUKA I TEKhNOLOGII ROSSII – STRF.ru, 2016 Kak ukrepit pozitsii rossiiskoi nauki v mire
15. A. N. Pechen, “On the speed gradient method for generating unitary quantum operations for closed quantum systems”, Russian Math. Surveys, 71:3 (2016), 597–599  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
16. 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  scopus
17. A. N. Pechen, N. B. Il'in, “On extrema of the objective functional for short-time generation of single-qubit quantum gates”, Izv. Math., 80:6 (2016), 1200–1212  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
18. Konstantin Lyakhov, Heon-Ju Lee, Alexander Pechen, “Some features of Boron isotopes separation by the laser-assisted retardation of condensation method in multipass irradiation cell implemented as a resonator”, IEEE Journal of Quantum Electronics, 52:12 (2016), 1400208 , 8 pp.  mathnet  crossref  isi  scopus
19. Oleg Lychkovskiy, Oleksandr Gamayun, Vadim Cheianov, Timescale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe, 2016 , 11 pp., arXiv: 1611.00663
20. O. Lychkovskiy, “Large quantum superpositions of a nanoparticle immersed in superfluid helium”, Phys. Rev. B, 93 (2016), 214517 , 4 pp.  mathnet  crossref  isi  scopus
21. Evgeny Kiktenko, Anton Trushechkin, Yury Kurochkin, Aleksey Fedorov, “Post-processing procedure for industrial quantum key distribution systems”, JPCS, 741:1 (2016), 12081 , 6 pp.  mathnet  crossref  isi (cited: 3)  elib  scopus (cited: 2)
22. E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, A. K. Fedorov, Symmetric blind information reconciliation for quantum key distribution, 2016 , 10 pp., arXiv: 1612.03673
23. E. O. Kiktenko, A. A. Popov, A. K. Fedorov, “Document Bidirectional imperfect quantum teleportation with a single Bell state”, Phys. Rev. A, 93:6 (2016), 62305 , 8 pp., arXiv: quant-ph/1602.01420  mathnet  crossref  isi (cited: 1)  scopus (cited: 2)
24. Aleksey Popov, Evgeny Kiktenko, Aleksey Fedorov, Vladimir I. Man'ko, “Information Processing Using Three-Qubit and QubitQutrit Encodings of Noncomposite Quantum Systems”, J. Russian Laser Research, 37:6 (2016), 581–590 , arXiv: quant-ph/1610.05576  mathnet  crossref  isi (cited: 1)  scopus

   2015
25. A. Pechen, A. Trushechkin, “Measurement-assisted Landau-Zener transitions”, Phys. Rev. A, 91:5 (2015), 052316 , 15 pp., arXiv: 1506.08323  mathnet  crossref  isi (cited: 4)  elib (cited: 2)  scopus (cited: 4)
26. A. N. Pechen, N. B. Il'in, “Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times”, Proc. Steklov Inst. Math., 289 (2015), 213–220  mathnet  crossref  crossref  isi (cited: 6)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 4)
27. 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 (cited: 5)  elib  scopus (cited: 4)
28. Cergei Dmitriev, Aleksandr Pechen, “Professionalnyi rost i nauchnaya karera: est li raznitsa?”, Elektronnoe izdanie NAUKA I TEKhNOLOGII ROSSII – STRF.ru, 2015 , 27 marta [Sergei Dmitriev and Alexander Pechen, The professional growth and scientific career: is there a difference? (in Russian), The electronic journal Science and Technology in RUSSIA – STRF.ru, 2015, March 27]
29. Aleksandr Pechen, Anna Gorbatova, “V SShA 56 avgusta vo vtoroi raz proshël Blavatnik Science Symposium”, Elektronnoe izdanie NAUKA I TEKhNOLOGII ROSSII – STRF.ru, 2015 , 10 avgusta [Alexander Pechen and Anna Gorbatova, The second annual Blavatnik Science Symposium took place on August 5th and 6th 2015 at the New York Academy of Sciences (USA), The electronic journal Science and Technology in RUSSIA - STRF.ru, 2015, August 10]
30. O. Lychkovskiy, “Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid”, Phys. Rev. A, 91 (2015), 040101 , 6 pp.  mathnet  crossref  isi (cited: 3)  scopus
31. O. Gamayun, O. Lychkovskiy, and V. Cheianov, “Reply to Comment on Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas”, Phys. Rev. E, 92 (2015), 016102 , 2 pp.  mathnet  crossref  isi (cited: 1)  scopus
32. S. M. Korotaev, E. O. Kiktenko, “Quantum causality in closed timelike curves”, Physica Scripta, 90 (2015), 085101 , 14 pp.  mathnet  crossref  isi  scopus
33. S. M. Korotaev, N. M. Budnev, V. O. Serdyuk, V. L. Zurbanov, R. R. Mirgazov, V. A. Machinin, E. O. Kiktenko, V. B. Buzin, A. V. Novysh, I. A. Portyanskaya, “Results of vertical electric field monitoring in Lake Baikal”, Izvestiya, Physics of the Solid Earth, 51:4 (2015), 602–611  mathnet  crossref  crossref  isi  elib  elib  scopus
34. E. O. Kiktenko, A. K. Fedorov, A. A. Strakhov, V. I. Man'ko, “Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits”, Physics Letters A, 379:22-23 (2015), 1409–1413 , arXiv: quant-ph/1503.01583  mathnet  crossref  zmath  isi (cited: 22)  scopus (cited: 20)
35. S. M. Korotaev N. M. Budnev V. O. Serdyuk V. L. Zurbanov R. R. Mirgazov V. S. Shneer V. A. Machinin E. O. Kiktenko V. B. Buzin A. I. Panfilov, “Recent results of monitoring of the vertical component of the electrical field in Lake Baikal on the surface-bed baseline”, Geomagnetism and Aeronomy, 55:3 (2015), 398–409  mathnet  crossref  isi  scopus
36. A. K. Fedorov, E. O. Kiktenko, O. V. Man'ko, V. I. Man'ko, “Tomographic discord for a system of two coupled nanoelectric circuits”, Physica Scripta, 90:5 (2015), 055101 , arXiv: quant-ph/1409.5265  mathnet  crossref  isi (cited: 7)  scopus (cited: 6)
37. E. O. Kiktenko, A. K. Fedorov, O. V. Man'ko, V. I. Man'ko, “Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities”, Physical Review A - Atomic, Molecular, and Optical Physics, 91 (2015), 042312 , 7 pp.  mathnet  crossref  isi (cited: 15)  scopus (cited: 23)
38. A. Fedorov, E. Kiktenko, “Mutual information-energy inequality for thermal states of a bipartite quantum system”, Journal of Physics: Conference Series, 594 (2015), 012045 , 5 pp.  mathnet  crossref  isi  scopus

   2014
39. A. N. Pechen, D. J. Tannor, “Control of quantum transmission is trap-free”, Canadian Journal of Chemistry, 92:2 (2014), 157–159 , arXiv: 1403.5700  mathnet  crossref  isi (cited: 3)  scopus (cited: 3)
40. Aleksandr Pechen, Nekotorye voprosy dinamiki i upravleniya kvantovymi sistemami, Veduschaya - Yana Rozova. Radio “Ekho Moskvy”. Peredacha “Moskva. Territoriya nauki” (sovmestno s Departamentom nauki, promyshlennoi politiki i predprinimatelstva g. Moskvy), 29 maya 2014 [Alexander Pechen, Some topics in dynamics and control of quantum systems (in Russian), Presenter Yana Rozova. In the broadcast Moscow. Territory of science on radio station Echo of Moscow (broadcast is organized jointly with Department of Science, Industrial Policy and Entrepreneurship of Moscow), May 29, 2014]
41. A. N. Pechen, N. B. Il'in, “Coherent control of a qubit is trap-free”, Proceedings of the Steklov Institute of Mathematics, 285 (2014), 233–240 , arXiv: 1407.5175  mathnet  crossref  crossref  isi (cited: 6)  elib  scopus (cited: 3)
42. O. Gamayun, O. Lychkovskiy, and V. Cheianov, “Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas”, Phys. Rev. E, 90 (2014), 032132 , 12 pp.  mathnet  crossref  isi (cited: 13)  scopus (cited: 13)
43. E. Burovski, V. Cheianov, O. Gamayun, and O. Lychkovskiy, “Momentum relaxation of a mobile impurity in a one-dimensional quantum gas”, Phys. Rev. A, 89 (2014), 041601 , 5 pp.  mathnet  crossref  isi (cited: 13)  scopus (cited: 10)  scopus (cited: 10)
44. O. Lychkovskiy, “Perpetual motion of a mobile impurity in a one-dimensional quantum gas”, Phys. Rev. A, 89 (2014), 033619 , 5 pp.  mathnet  crossref  isi (cited: 9)  scopus (cited: 8)
45. D. A. Kronberg, S. N. Molotkov, “Duality of quantum communication channels and a collective intercept-resend attack on quantum key distribution with differential phase shift”, JETP Letters, 100:4 (2014), 279–284  mathnet  crossref  crossref  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
46. D. A. Kronberg, S. N. Molotkov, “On a beam splitter attack and soft filtering of coherent states in differential phase shift quantum cryptography”, Journal of Experimental and Theoretical Physics, 118:1 (2014), 1–10  mathnet  crossref  crossref  isi (cited: 2)  scopus (cited: 1)
47. D. A. Kronberg, “A simple coherent attack and practical security of differential phase shift quantum cryptography”, Laser Physics, 24:2 (2014), 025202 , 4 pp.  mathnet  crossref  isi  scopus
48. Kiktenko E.O, Fedorov A.K, “Tomographic causal analysis of two-qubit states and tomographic discord”, Physics Letters, Section A: General, Atomic and Solid State Physics, 378:24–25 (2014), 1704–1710  mathnet  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 5)
49. Kiktenko E.O., Korotaev S.M., “Causality in different formalisms of quantum teleportation treatment”, Physics Essays, 27:4 (2014), 548–553  mathnet  crossref  scopus (cited: 1)

   2013
50. Aleksandr Pechen, “Reformy, no ne takie”, Polit.ru, 04 iyulya 2013 Reformy, no ne takie [Alexander Pechen, The reforms, but not like these (in Russian), Electronic media Polit.ru, 2013, July 04]
51. A.N. Pechen, N.B. Il'in, “Control of two-level quantum systems by measurements”, Trudy mezhdunarodnoi shkoly-konferentsii “Upravlenie i optimizatsiya negolonomnykh sistem” (Pereslavl Zalesskii, Rossiya, 10-13 iyulya 2013 g.), Universitet g. Pereslavlya, 2013, 49–50
52. A.N. Pechen, “Recent advances in the analysis of quantum control landscapes”, Trudy mezhdunarodnoi konferentsii “Matematicheskaya teoriya upravleniya i mekhanika” (Suzdal, Rossiya, 5–9 iyulya 2013 g.), MIAN, 2013, 276–277
53. A. N. Pechen, “Introduction to some topics in modern quantum control”, Trudy mezhdunarodnoi shkoly-konferentsii “Upravlenie i optimizatsiya negolonomnykh sistem” (Pereslavl-Zalesskii, Rossiya, 10–13 iyulya 2013 g.), Universitet goroda Pereslavlya, 2013, 22–24
54. A. N. Pechen, Nekotorye voprosy dinamiki i upravleniya kvantovymi sistemami, Diss. … dokt. fiz.-matem. nauk, Matematicheskii institut im. V.A. Steklova Rossiiskoi akademii nauk, Moskva, 2013 , 194 pp. www.mi.ras.ru/dis/ref13/pechen_diss_v2.pdf
55. E. Safonov, O. Lychkovskiy, “Spin dynamics in finite cyclic XY model”, Phys. Rev. A, 87 (2013), 042105 , 19 pp.  mathnet  crossref  isi (cited: 3)  scopus (cited: 2)
56. O. Lychkovskiy, “Dependence of decoherence-assisted classicality on the way a system is partitioned into subsystems”, Phys. Rev. A, 87 (2013), 022112 , 7 pp.  mathnet  crossref  isi (cited: 6)  scopus (cited: 10)
57. Fedorov A.K., Kiktenko E.O., “Quaternion Representation and Symplectic Spin Tomography”, Journal of Russian Laser Research, 34:5 (2013), 477–487  mathnet  crossref  isi (cited: 3)  scopus (cited: 3)
58. Kiktenko E.O., Korotaev S.M., “Entanglement and causality in the interaction of the two-level atom with the field”, Physica Scripta, 88:5 (2013), 055008  mathnet  crossref  isi (cited: 4)  scopus (cited: 2)
59. Korotaev S.M., Kiktenko E.O., Gaidash S.P., Budnev N.M., Mirgazov R.R., Panfilov A.I., Khalezov A.A., Serdyuk V.O., Shneer V.S., “Relationship between variations in the electric field's vertical component in Lake Baikal and solar activity”, Geomagnetism and Aeronomy, 53:6 (2013), 769–773  mathnet  crossref  crossref  isi (cited: 2)  scopus (cited: 2)

   2012
60. X.-J. Feng, A. Pechen, A. Jha, R. Wu, H. Rabitz, “Global optimality of fitness landscapes in evolution”, Chemical Science, 3 (2012), 900–906 , Edge Article  mathnet  crossref  isi (cited: 2)  elib  scopus (cited: 2)
61. A. Pechen, “Quantum measurements as a control resource”, OSA Technical Digest (Berlin, Germany, March 19–21, 2012), Optical Society of America, 2012, QW2A.8 , arXiv: 1508.04249
62. A. Pechen, N. Il'in, “Trap-free manipulation in the Landau-Zener system”, Phys. Rev. A, 86 (2012), 052117 , 6 pp., arXiv: 1304.1357  mathnet  crossref  adsnasa  isi (cited: 10)  scopus (cited: 10)
63. A. Pechen, “Incoherent light as a control resource”, OSA Technical digest (Berlin, Germany, March 19–21, 2012), Optical Society of America, 2012, JT2A.23 , arXiv: 1212.2253
64. A. N. Pechen, D. J. Tannor, “Quantum control landscape for a Lambda-atom in the vicinity of second-order traps”, Israel Journal of Chemistry, 52:5 (2012), 467–472 , arXiv: 1508.04169  mathnet  crossref  isi (cited: 6)  scopus (cited: 7)
65. A. N. Pechen, D. J. Tannor, “Pechen and Tannor Reply”, Phys. Rev. Lett., 108 (2012), 198902 , 1 pp.  crossref
66. B. Leggio, O. Lychkovskiy, A. Messina, “On the merit of a Central Limit Theorem-based approximation in statistical physics”, J. Stat. Phys., 146 (2012), 1274–1287  mathnet  crossref  mathscinet  zmath  isi  scopus
67. J. Exp. Theor. Phys., 114:3 (2012), 382–391  mathnet  crossref  isi  scopus
68. Korotaev S.M., Kiktenko E.O., “Causality and decoherence in the asymmetric states”, Physica Scripta, 85:5 (2012), 055006  mathnet  crossref  isi (cited: 4)  scopus (cited: 5)
69. Kiktenko E.O., Korotaev S.M., “Causal analysis of asymmetric entangled states under decoherence”, Physics Letters, Section A: General, Atomic and Solid State Physics, 376:6–7 (2012), 820–823  mathnet  crossref  mathscinet  zmath  isi (cited: 6)  scopus (cited: 7)

   2011
70. K. W. Moore, A. Pechen, X.-J. Feng, J. Dominy, V. Beltrani, H. Rabitz, “Universal characteristics of chemical synthesis and property optimization”, Chemical Science, 2:3 (2011), 417–424 , Edge Article  crossref  isi (cited: 15)  elib (cited: 6)  scopus (cited: 15)
71. A. N. Pechen, D. J. Tannor, “Are there traps in quantum control landscapes?”, Phys. Rev. Lett., 106 (2011), 120402 , 3 pp., This paper has been selected for the Editor's choice section of Science magazine, vol. 332, p. 514 (29 April 2011): “Look Out for Traps”, by Jake S. Yeston, arXiv: 1508.05434  crossref  adsnasa  isi (cited: 40)  scopus (cited: 38)
72. K. W. Moore, A. Pechen, X.-J. Feng, J. Dominy, V.J. Beltrani, H. Rabitz, “Why is chemical synthesis and property optimization easier than expected?”, Physical Chemistry Chemical Physics, 13:21 (2011), 10048–10070 , Perspective article  crossref  isi (cited: 24)  scopus (cited: 24)
73. A. N. Pechen, “Some topics in dynamics and control of open quantum systems”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2(23) (2011), 155–161  mathnet  crossref  rsci
74. A. Pechen, “Engineering arbitrary pure and mixed quantum states”, Phys. Rev. A, 84:4 (2011), 042106 , 6 pp., arXiv: 1210.2281  crossref  adsnasa  isi (cited: 9)  scopus (cited: 12)
75. A. Pechen, “Selected topics in dynamics and control of open quantum systems”, P-Adic Numbers, Ultrametric Analysis and Applications, 3:3 (2011), 248–252  crossref  mathscinet
76. A. N. Pechen, “Critical points of objective functions for quantum control problems”, Tambov University Reports, 16:4 (2011), 1146–1148  elib
77. A. N. Pechen, Kh. Rabits, “Nekogerentnoe upravlenie otkrytymi kvantovymi sistemami”, Sovremennaya matematika. Fundamentalnye napravleniya, 42, 2011, 179–185  mathnet (cited: 1)  mathscinet; A. Pechen, H. Rabitz, “Incoherent control of open quantum systems”, Journal of Mathematical Sciences, 199:6 (2014), 695–701  crossref  mathscinet  elib (cited: 1)  scopus (cited: 1)
78. O. Lychkovskiy, “Entanglement and Relaxation in Exactly Solvable Models”, Optics and Spectroscopy, 111 (2011), 713–721  crossref  isi  scopus
79. O. Lychkovskiy, “Entanglement, decoherence and thermal relaxation in exactly solvable models”, J. Phys. Conf. Ser., 306 (2011), 012028 , 7 pp.  crossref  isi (cited: 2)  scopus (cited: 2)
80. D. A. Kronberg, “Rasshirenie oblasti sekretnosti protokola kvantovogo raspredeleniya klyuchei s fazovo-vremennym kodirovaniem”, Sbornik statei molodykh uchenykh fakulteta VMK MGU, Izdatelskii otdel fakulteta VMK MGU, 2011, 69–82
81. D. A. Kronberg, Yu. I. Ozhigov, A. Yu. Chernyavskii, Kvantovaya kriptografiya, Maks Press, Moskva, 2011 , 112 pp. http://sqi.cs.msu.su/store/storage/ss8dw5n_quantum_cryptography.pdf
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