Noncommutative probability, quantum information and statistical decision theory, mathematical statistics of random processes.
Mathematical theory of quantum communication channels was developed, coding theorems of quantum information theory were established, noncommutative statistical decision theory was constructed, the structure of quantum Markov processes was investigated.
Biography
Graduated from the Moscow Institute of Physics and Technology in 1966, dyploma in «Applied mathematics and computer science». From 1969 works in the Steklov Mathematical Institute, Moscow. Candidate of phys-math sciences — 1969, Doctor of of phys-math sciences — 1975, Professor — 1986. List of publications contains nearly 190 titles including five monographs, four of them translated into English and published by the leading foreign Publishing houses (AMS, North Holland, Springer-Verlag). Awards: A. A. Markov Prize, Russian Academy of Sciences for the series of works on the noncommutative probability theory — 1997; Awards of the Russian Academy of Sciences for the best research achievements in 1992, 1995, 2008, 2015; International «Quantum Communication Award» — 1996; A. von Humboldt Research Award — 1999;
Claude E. Shannon Award 2016. Invited speaker at the International Congresses of Mathematicians — Berkeley (1986), Madrid (2006), and many other international and national conferences. Member of the Editorial boards of the journals: «Theory of probability and its applications», «Russian mathematical surveys (Uspekhi)», «Sbornik:mathematics», «Theoretical and mathematical physics», «Izvestiya vuzov: Mathematics», «IEEE Transactions on Information Theory», «Quantum Information Processing», «Reports on Mathematical Physics».
Main publications:
A. S. Holevo, Studies in general theory of statistical decisions, Proc. Steklov Math. Inst., 124, 1978
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, North Holland, 1982
A. S. Holevo, Statistical structure of quantum theory, Lect. Notes Phys., 67, Springer, 2001
A. S. Holevo, Quantum systems, channels, information, DeGruyter, 2012
A. S. Holevo, “Quantum dynamical semigroups: Nonstandard generators, stochastic representations”, Abstracts of talks given at the 3rd International conference on stochastica methods (Novorossijsk, June 3–9, 2018), Theory Probab. Appl., 64 (2019), 140–141
3.
A. S. Kholevo, “Generators of quantum one-dimensional diffusions”, Theory Probab. Appl., 64:2 (2019), 249–263
4.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction., 2nd ed., extended and complemented, De Gruyter, Berlin–Boston, 2019 , xv+350 pp.
5.
A. S. Holevo, Gaussian maximizers for quantum Gaussian observables and ensembles, 2019 , 16 pp., arXiv: 1908.03038
6.
A. S. Holevo, A. A. Kuznetsova, Information capacity of continuous variable measurement channel, 2019 , 17 pp., arXiv: 1910.05062
7.
M. E. Shirokov, A. S. Holevo, “Energy-constrained diamond norms and quantum dynamical semigroups”, Lobachevskii J. Math., 40:10 (2019), 1569–1586
8.
A. S. Kholevo, “Kvantovaya informatika”, sb. “Matematicheskaya sostavlyayuschaya”, 2019, 38–39
A. S. Holevo, “Mathematical foundations of quantum informatics”, Lekts. Kursy NOC, 30, 2018, 3–118
2017
11.
M. E. Shirokov, A. S. Holevo, “On lower semicontinuity of the entropic disturbance and its applications in quantum information theory”, Izv. Math., 81:5 (2017), 1044–1060 (cited: 2) (cited: 1)
2018
12.
A. S. Holevo, “ON THE CLASSICAL CAPACITY OF A CHANNEL WITH STATIONARY QUANTUM GAUSSIAN NOISE”, THEORY PROBAB. APPL., 62:4 (2018), 534–551
2017
13.
I. Siemon, A. S. Holevo, R. F. Werner, “Unbounded generators of dynamical semigroups”, Open Syst. Inf. Dyn., 24:4 (2017), 1740015 , 24 pp. (cited: 4) (cited: 4)
14.
A. S. Holevo, “On the quantum Gaussian optimizers conjecture in the case $q=p$”, Russian Math. Surveys, 72:6 (2017), 1177–1179 (cited: 2) (cited: 2)
2016
15.
A. S. Holevo, “On the constrained classical capacity of infinite-dimensional covariant quantum channels”, J. Math. Phys., 57:1 (2016), 15203 , 11 pp. (cited: 1) (cited: 5) (cited: 5)
16.
A. S. Holevo, “On the proof of the majorization theorem for quantum Gaussian channels”, Russian Math. Surveys, 71:3 (2016), 585–587 (cited: 1) (cited: 1)
2017
17.
A. S. Holevo, “On a characterization of Gaussian transition operators”, Theory Probab. Appl., 61:4 (2017), 715–718
2016
18.
A. S. Holevo, “The classical capacity of quantum Gaussian gauge-covariant channels: beyond i.i.d.”, IEEE Information Theory Society Newsletter, 66:4 (2016), 3–6
V. Giovannetti, A. S. Holevo, R. García-Patrón, “A solution of Gaussian optimizer conjecture for quantum channels”, Comm. Math. Phys., 334:3 (2015), 1553–1571 (cited: 10) (cited: 36) (cited: 8)
21.
V. Giovannetti, A. S. Holevo, A. Mari, “Majorization and additivity for multimode bosonic Gaussian channels”, Theoret. and Math. Phys., 182:2 (2015), 284–293 (cited: 14) (cited: 5) (cited: 5) (cited: 14)
22.
A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367 (cited: 24) (cited: 1) (cited: 1) (cited: 16)
23.
A. S. Holevo, M. E. Shirokov, “On the Gain of Entanglement Assistance in the Classical Capacity of Quantum Gaussian Channels”, Math. Notes, 97:6 (2015), 974–977 (cited: 1) (cited: 1)
24.
G. De Palma, A. Mari, V. Giovannetti, A. S. Holevo, “Normal form decomposition for Gaussian-to-Gaussian superoperators”, J. Math. Phys., 56:5 (2015), 052202 , 19 pp. (cited: 3) (cited: 10) (cited: 14)
2016
25.
A. S. Holevo, M. E. Shirokov, “Criterion of weak compactness for families of generalized quantum ensembles and its corollaries”, Theory Probab. Appl., 60:2 (2016)
2014
26.
Y. I. Bogdanov, B. I. Bantysh, V. F. Lukichev, A. A. Orlikovsky, A. S. Holevo, “Entanglement dynamics in quantum operations using superconducting phase qubits”, Bulletin of the Russian Academy of Sciences: Physics, 78:1 (2014), 1–5 (cited: 1) (cited: 1) (cited: 1)
27.
A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14 (cited: 1)
2015
28.
A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels. II”, Theory Probab. Appl., 59:1 (2015), 145–154
2014
29.
A. Mari, V. Giovannetti, A. S. Holevo, “Quantum state majorization at the output of bosonic Gaussian channels”, Nature Communications, 5 (2014), 3826 , 5 pp. (cited: 46) (cited: 44)
30.
V. Giovannetti, R. Garcia-Patron, N. J. Cerf, A. S. Holevo, “Ultimate classical communication rates of quantum optical channels”, Nature Photonics, 8:10 (2014), 216 , 6 pp. (cited: 77) (cited: 23)
31.
A. S. Holevo, “Quantum Gaussian optimizer problem”, New Horizons in Statistical Decision Theory (Oberwolfach, 7–13 September 2014), Oberwolfach Reports, 41/2014, Mathematisches Forschungsinstitut Oberwolfach, 2014, 28–31
2013
32.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction, De Gruyter, Berlin–Boston, 2013 , 370 pp. (rasshirennoe i ispravlennoe izdanie angliiskogo perevoda monografii)
33.
A. S. Holevo, “Information capacities of quantum measurement channels”, 19e Tsentralno-evropeiskoe soveschanie po kvantovoi optike (Sinaia, Romania, 2–6.07.2012), Phys. Scr., T153, 2013, 014034 , 4 pp. (cited: 8) (cited: 5) (cited: 7)
34.
A. S. Holevo, “Extreme bosonic linear channels”, Theoret. and Math. Phys., 174:2 (2013), 288–297 (cited: 9) (cited: 5) (cited: 5) (cited: 7)
35.
A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31 (cited: 11) (cited: 4) (cited: 10)
36.
A. S. Holevo, “Capacities of Gaussian classical-quantum channels”, Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on (Istanbul, Turkey, July 7–12 2013), IEEE, 2013, 176–180
2014
37.
A. A. Kuznetsova, A. S. Holevo, “Coding Theorems for Hybrid Channels”, Theory Probab. Appl., 58:2 (2014), 264–285 (cited: 1) (cited: 1) (cited: 1) (cited: 1)
2013
38.
V. Giovannetti, A. S. Holevo, R. Garcia-Patron, A solution of the Gaussian optimizer conjecture, 2013 , 24 pp., Newton Institute preprint NI13068-MQI, arXiv: 1312.2251
2012
39.
A. S. Holevo, V. Giovannetti, “Quantum channels and their entropic characteristics”, Rep. Prog. Phys., 75 (2012), 046001 , 45 pp. (cited: 79) (cited: 35) (cited: 83)
40.
A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10 (cited: 25) (cited: 18) (cited: 27)
2011
41.
A. S. Holevo, “Entropy gain and the Choi–Jamiolkowski correspondence for infinite-dimensional quantum evolutions”, Theoret. and Math. Phys., 166:1 (2011), 123–138 (cited: 24) (cited: 11) (cited: 11) (cited: 24)
42.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, 2nd edition, Edizioni della Normale, Pisa, 2011
43.
F. Caruso, J. Eisert, V. Giovannetti, A. S. Holevo, “The optimal unitary dilation for bosonic Gaussian channels”, Phys. Rev. A, 84 (2011), 022306 , 10 pp. (cited: 16) (cited: 10) (cited: 18)
44.
A. S. Holevo, “The Choi-Jamiolkowski forms of quantum Gaussian channels”, J. Math. Phys., 52 (2011), 042202 , 12 pp. (cited: 19) (cited: 8) (cited: 21)
45.
A. S. Kholevo, “Klassicheskaya i kvantovaya entropii kak mery informatsii”, Trudy Mezhdunarodnykh nauchnykh konferentsii «Situatsionnye tsentry i informatsionno-analiticheskie sistemy klassa 4i» (Moskva, 14–16 noyabrya 2011 g.), Izd-vo IFTI, Moskva–Protvino, 2011, 1–5
46.
A. S. Holevo, “The entropy gain of quantum channels”, IEEE International Symposium on Information Theory (ISIT) (Jule 31 – August 05, 2011, St. Petersburg, Russia), 2011, 289–292 (cited: 2)
47.
A. S. Holevo, “Statistical inference for quantum systems”, International Encyclopedia of Statistical Science, eds. M. Lovric, Springer, 2011, 1420–1423
2010
48.
A. S. Kholevo, Kvantovye sistemy, kanaly, informatsiya, MTsNMO, M., 2010 , 328 pp. https://www.mccme.ru/free-books/holevo-quantum.pdf
49.
A. S. Holevo, “Two mathematical problems of quantum information theory”, Mathematical horizons for quantum physics, Lecture Note Series, Institute for Mathematical Sciences, National University of Singapore, 20, World Scientific, 2010, 109–131
50.
A. S. Holevo, “The entropy gain of infinite-dimensional quantum evolutions”, Dokl. Math., 82:2 (2010), 730–731 (cited: 17) (cited: 5) (cited: 5) (cited: 18)
51.
A. S. Kholevo, “Kvantovaya teoriya informatsii. Kanaly i propusknye sposobnosti”, Informatsionnye tekhnologii i vychislitelnye sistemy, 3 (2010), 39–46
52.
A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218 (cited: 12) (cited: 8) (cited: 13)
53.
V. Giovannetti, A. S. Holevo, S. Lloyd, L. Maccone, “Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results”, J. Phys. A, 43:41 (2010), 415305 , 10 pp. (cited: 19) (cited: 16) (cited: 22)
54.
T. Heinosaari, A. S. Holevo, M. M. Wolf, “The semigroup structure of Gaussian channels”, Quantum Inf. Comput., 10:7-8 (2010), 619–635 (cited: 23) (cited: 6) (cited: 23)
2009
55.
A. S. Holevo, J.-P. Pellonpää, “Extreme Covariant Observables for Type I Symmetry Groups”, Found. Phys., 39:6 (2009), 625–641 (cited: 5) (cited: 3) (cited: 5)
56.
A. S. Kholevo, “Kvantovaya teoriya informatsii”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 451–453
57.
A. S. Kholevo, K. A. Valiev, “Kvantovyi kompyuter”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 472–473
2008
58.
F. Caruso, J. Eisert, V. Giovannetti, A. S. Holevo, “Multi-mode bosonic Gaussian channels”, New J. Phys., 10 (2008), 083030 , 33 pp. (cited: 53) (cited: 56)
59.
A. S. Holevo, V. Giovannetti, “Quantum shared broadcasting”, Quantum Inf. Process., 7:2-3 (2008), 55–69 (cited: 5) (cited: 5) (cited: 5)
60.
A. S. Holevo, “Entanglement-Breaking Channels in Infinite Dimensions”, Problems Inform. Transmission, 44:3 (2008), 171–184 (cited: 61) (cited: 38) (cited: 38) (cited: 73)
61.
M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90 (cited: 37) (cited: 8) (cited: 8) (cited: 22)
62.
A. S. Kholevo, “Kvantovaya informatika: proshloe, nastoyaschee, buduschee”, V mire nauki, 2008, no. 7, 68–75http://www.sciam.ru/2008/7/inform.shtml (cited: 1)
2007
63.
A. S. Holevo, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11 (cited: 72) (cited: 42) (cited: 42) (cited: 72)
2006
64.
A. S. Holevo, “The additivity problem in quantum information theory”, International Congress of Mathematicians, Vol. III, Eur. Math. Soc., Zürich, 2006, 999–1018
65.
N. Datta, M. Fukuda, A. S. Holevo, “Complementarity and additivity for covariant channels”, Quantum Inf. Process., 5:3 (2006), 179–207 (cited: 21) (cited: 10) (cited: 21)
66.
F. Caruso, V. Giovannetti, A. S. Holevo, “One-mode Bosonic Gaussian channels: a full weak-degradability classification”, New Journal of Physics, 8 (2006), 310 , 23 pp. (cited: 72) (cited: 72)
67.
A. S. Holevo, “Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory”, Russian Math. Surveys, 61:2 (2006), 301–339 (cited: 12) (cited: 3) (cited: 3) (cited: 10)
2007
68.
A. S. Holevo, “Complementary channels and the additivity problem”, Theory Probab. Appl., 51:1 (2007), 92–100 (cited: 31) (cited: 13) (cited: 13) (cited: 21)
2006
69.
A. S. Holevo, “Locating a photon:position observables and an uncertainty relation”, Russian Microelectronics, 35:1 (2006), 21–30
70.
N. Datta, A. S. Holevo, Yu. M. Suhov, “Additivity for transpose depolarizing channels”, Int. J. Quant. Inform.,, 4:1 (2006), 85–98 (cited: 13) (cited: 4) (cited: 11)
71.
A. S. Holevo, “Quantum channels: classical capacity”, Encyclopedia of Mathematical Physics, Academic Press, 2006, 142–144
2005
72.
R. F. Werner, A. S. Holevo, M. E. Shirokov, “On the notion of entanglement in Hilbert spaces”, Russian Math. Surveys, 60:2 (2005), 359–360 (cited: 19) (cited: 26)
73.
N. Datta, A. S. Holevo, Yu. M. Sukhov, “On a Sufficient Additivity Condition in Quantum Information Theory”, Problems Inform. Transmission, 41:2 (2005), 76–90 (cited: 3) (cited: 3) (cited: 7)
74.
A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98 (cited: 32) (cited: 22) (cited: 22) (cited: 28)
75.
A. S. Holevo, “The additivity problem and constrained quantum channels”, Proc. Int. Soc. Opt. Eng., 5833 (2005), 196–201
76.
A. S. Holevo, “Additivity conjecture and covariant channels”, Int. J. Quant., 3:1 (2005), 41–48 (cited: 18) (cited: 12) (cited: 19)
77.
A. S. Holevo, “Multiplicativity of norms of maps in $S_p$ spaces and related problems of quantum information theory”, Mezhdunarodnaya konferentsiya "Funktsionalnye prostranstva, teoriya priblizhenii, nelineinyi analiz, posvyaschennaya stoletiyu S. M. Nikolskogo. Tezisy dokladov (Moskva, 23-29 maya 2005 g.), RAN, 2005, 294
2004
78.
A. S. Holevo, M. E. Shirokov, “On Shor's channel extension and constrained channels”, Comm. Math. Phys., 249:2 (2004), 417–430 (cited: 26) (cited: 29) (cited: 29)
79.
A. S. Holevo, M. E. Shirokov, “The additivity problem for constrained quantum channels”, Russian Math. Surveys, 59:2 (2004), 385–387
2005
80.
A. S. Holevo, “Asymptotic estimation of a shift parameter of a quantum state”, Theory Probab. Appl., 49:2 (2005), 207–220 (cited: 4) (cited: 4) (cited: 5)
2003
81.
A. S. Holevo, “Quantum and classical stochastic calculus”, Quantum probability communications (Grenoble, 1998), Vol. XI, QP-PQ, XI, World Sci. Publ., River Edge, NJ, 2003, 199–219
82.
A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, 2-e izd., Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003 , 410 pp.
83.
A. S. Kholevo, Statisticheskaya struktura kvantovoi teorii, Institut kompyuternykh issledovanii, Izhevsk, 2003 , 192 pp.
2004
84.
A. S. Holevo, “Entanglement-assisted capacities of constrained quantum channels”, Theory Probab. Appl., 48:2 (2004), 243–255 (cited: 12) (cited: 13) (cited: 21)
2003
85.
A. S. Holevo, “Optimal receiver of a binary coherent signals based on the principle of optical feedback”, Laser Physics, 13:12 (2003), 1558–1561 (cited: 12) (cited: 2) (cited: 2)
2004
86.
A. A. Borovkov, V. A. Vatutin, V. M. Zolotarev, A. M. Zubkov, I. A. Ibragimov, R. I. Ivanovskaya, V. F. Kolchin, V. P. Maslov, Yu. V. Prokhorov, M. V. Khatuntseva, V. I. Khokhlov, A. S. Holevo, D. M. Chibisov, A. N. Shiryaev, “On the 80th Birthday of B. A. Sevastyanov”, Theory Probab. Appl., 48:4 (2004), 697–702
2002
87.
A. S. Holevo, “On states, channels, and purification”, Quantum Inf. Process., 1:1-2 (2002), 1–4 (cited: 1)
88.
R. F. Werner, A. S. Holevo, “Counterexample to an additivity conjecture for output purity of quantum channels”, Quantum information theory, J. Math. Phys., 43, no. 9, 2002, 4353–4357 (cited: 94) (cited: 82) (cited: 97)
89.
A. S. Holevo, “On entanglement-assisted classical capacity”, Quantum information theory, J. Math. Phys., 43, no. 9, 2002, 4326–4333 (cited: 53) (cited: 55)
90.
A. S. Kholevo, Vvedenie v kvantovuyu teoriyu informatsii, MTsNMO, M., 2002 , 128 pp.
2003
91.
G. G. Amosov, A. S. Holevo, “On the multiplicativity hypothesis for quantum communication channels”, Theory Probab. Appl., 47:1 (2003), 123–127 (cited: 10) (cited: 6) (cited: 9)
2002
92.
A. S. Holevo, “Erratum: “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory” [Math. Methods Statist. 10 (2001), no. 1, 6–22]”, Math. Methods Statist., 11:1 (2002), 133
2001
93.
A. S. Holevo, Statistical structure of quantum theory, Lecture Notes in Physics. Monographs, 67, Springer-Verlag, Berlin, 2001 , x+159 pp.
94.
A. S. Holevo, “Coding theorems of quantum information theory”, XIIIth International Congress on Mathematical Physics (London, 2000), Int. Press, Boston, MA, 2001, 415–422
95.
A. S. Holevo, “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory”, Math. Methods Statist., 10:1 (2001), 6–22
96.
A. S. Holevo, “An invitation to quantum estimation”, Math. Methods Statist., 10:1 (2001), 1–5
97.
A. S. Holevo, “Lévy processes and continuous quantum measurements”, Lévy processes, Birkhäuser Boston, Boston, MA, 2001, 225–239
98.
A. S. Holevo, R. F. Werner, “Evaluating capacities of Bosonic Gaussian channels”, Phys. Rev. A, 63 (2001), 032312 , 13 pp. (cited: 293) (cited: 79)
99.
A. S. Holevo, G. G. Amosov, R. F. Werner, “On additivity/multiplicativity problems for quantum channels”, Proc. 5-th International Conference on Quantum Communication, Computing and Measurement (Capri, 03-08.07.2000), eds. O. Hirota, P. Tombesi, Kluver/Plenum Press, New York- London, 2001, 3–10
2000
100.
A. S. Holevo, M. Sohma, O. Hirota, “Error exponents for quantum channels with constrained inputs”, Rep. Math. Phys., 46:3 (2000), 343–358 (cited: 9) (cited: 9) (cited: 11)
101.
A. S. Holevo, “Reliability function of general classical-quantum channel”, IEEE Trans. Inform. Theory, 46:6 (2000), 2256–2261 (cited: 32) (cited: 17) (cited: 34)
102.
G. G. Amosov, A. S. Holevo, R. F. Werner, “On the Additivity Conjecture in Quantum Information Theory”, Problems Inform. Transmission, 36:4 (2000), 305–313
1999
103.
A. S. Holevo, M. Sohma, O. Hirota, “The capacity of quantum Gaussian channels”, Phys. Rev. A, 59:3 (1999), 1820–1828 (cited: 161) (cited: 135) (cited: 163)
104.
A. S. Holevo, “Sending quantum information with Gaussian states”, Proc. of the Fourth International Conference on Quantum Communication, Computing and Measurement (Evanston, 22–27.08.1998), eds. P. Kumar, M. D'Ariano and O. Hirota, Plenum Press, New York–London, 1999, 75–82
105.
M. V. Burnashev, A. S. Holevo, “Letter to the Editor”, Problems Inform. Transmission, 35:1 (1999), 93–94
1998
106.
A. S. Holevo, “Generalized imprimitivity systems and canonical conjugateness in quantum mechanics”, Quantization, coherent states, and Poisson structures (Białowieża, 1995), PWN, Warsaw, 1998, 207–218
107.
A. S. Holevo, “Covariant quantum dynamical semigroups: unbounded generators”, Irreversibility and causality (Goslar, 1996), Lecture Notes in Phys., 504, Springer, Berlin, 1998, 67–81
108.
A. S. Holevo, “Radon-Nikodým derivatives of quantum instruments”, J. Math. Phys., 39:3 (1998), 1373–1387 (cited: 24) (cited: 21) (cited: 24)
109.
A. S. Holevo, “The capacity of the quantum channel with general signal states”, IEEE Trans. Inform. Theory, 44:1 (1998), 269–273 (cited: 652) (cited: 539) (cited: 695)
110.
A. S. Holevo, “Quantum coding theorems”, Russian Math. Surveys, 53:6 (1998), 1295–1331 (cited: 119) (cited: 66) (cited: 131)
111.
M. V. Burnashev, A. S. Holevo, “On the Reliability Function for a Quantum Communication Channel”, Problems Inform. Transmission, 34:2 (1998), 97–107
1999
112.
A. S. Holevo, “International symposium on information theory 1998”, Theory Probab. Appl., 43:4 (1999), 685–686
1997
113.
A. S. Holevo, “On covariant instruments in quantum measurement theory”, Quantum Communication, Computing and Measurement. Proc. of the Third International Conference (Shizuoka, 25-30.09.1996.), eds. O. Hirota, A. S. Holevo and C. Caves, Plenum Press, New York - London, 1997, 223–232
1996
114.
A. S. Holevo, “The structure of classical noise”, Analysis, geometry and probability, Texts Read. Math., 10, Hindustan Book Agency, Delhi, 1996, 73–86
115.
A. S. Holevo, “Stochastic differential equations in Hilbert space and quantum Markovian evolutions”, Probability theory and mathematical statistics (Tokyo, 1995), World Sci. Publ., River Edge, NJ, 1996, 122–131
116.
A. S. Holevo, “Exponential formulae in quantum stochastic calculus”, Proc. Roy. Soc. Edinburgh Sect. A, 126:2 (1996), 375–389 (cited: 5) (cited: 8)
117.
A. S. Holevo, “On dissipative stochastic equations in a Hilbert space”, Probab. Theory Related Fields, 104:4 (1996), 483–500 (cited: 35) (cited: 29) (cited: 34)
118.
A. S. Holevo, “Covariant quantum Markovian evolutions”, J. Math. Phys., 37:4 (1996), 1812–1832 (cited: 43) (cited: 44)
119.
A. S. Holevo, M. Sasaki, T. S. Usuda, O. Hirota, “Application of the Jaynes-Kummings model for the detection of nonorthogonal quantum states”, Phys. Rev. A, 53 (1996), 1273–1279 (cited: 17)
120.
A. S. Holevo, “There exists a non-standard dynamical semigroup on $\mathfrak L(\mathscr H)$”, Russian Math. Surveys, 51:6 (1996), 1206–1207 (cited: 1) (cited: 3)
121.
B. M. Gurevich, I. A. Ibragimov, R. A. Minlos, I. A. Ovseevich, V. I. Oseledets, M. S. Pinsker, V. V. Prelov, Yu. V. Prokhorov, Ya. G. Sinai, A. S. Kholevo, A. N. Shiryaev, “Roland Lvovich Dobrushin (20.VII.1929–12.XI.1995)”, TVP, 41:1 (1996), 164–169; B. M. Gurevich, I. A. Ibragimov, R. A. Minlos, I. A. Ovseevich, V. I. Oseledets, M. S. Pinsker, V. V. Prelov, Yu. V. Prokhorov, Ya. G. Sinai, A. S. Holevo, A. N. Shiryaev, “Roland L'vovich Dobrushin (20 July 1919 – 12 November 1995)”, Theory Probab. Appl., 41:1 (1997), 132–136
1995
122.
A. Barchielli, A. S. Holevo, “Constructing quantum measurement processes via classical stochastic calculus”, Stochastic Process. Appl., 58:2 (1995), 293–317 (cited: 47) (cited: 19) (cited: 49)
123.
A. S. Holevo, “On the structure of covariant dynamical semigroups”, J. Funct. Anal., 131:2 (1995), 255–278 (cited: 25) (cited: 21)
124.
A. S. Holevo, “On translation-covariant quantum Markov equations”, Izv. Math., 59:2 (1995), 427–443 (cited: 19)
125.
A. S. Holevo, “Excessive maps, “arrival times” and perturbation of dynamical semigroups”, Izv. Math., 59:6 (1995), 1311–1325 (cited: 3)
1993
126.
A. S. Holevo, “A note on covariant dynamical semigroups”, Rep. Math. Phys., 32:2 (1993), 211–216 (cited: 10) (cited: 44)
127.
A. S. Holevo, “On conservativity of covariant dynamical semigroups” (Toruń, 1992), Rep. Math. Phys., Proceedings of the XXV Symposium on Mathematical Physics, 33, no. 1-2, 1993, 95–110 (cited: 7) (cited: 25)
128.
A. S. Kholevo, “Structure of covariant dynamical semigroups”, Russian Acad. Sci. Dokl. Math., 47:1 (1993), 161–167
129.
A. Barchielli, A. S. Holevo, G. Lupieri, “An analogue of Hunt's representation theorem in quantum probability”, J. Theoret. Probab., 6:2 (1993), 231–265 (cited: 1) (cited: 9)
130.
A. S. Kholevo, “On the Lévy–Khinchin formula in noncommutative probability theory”, Theory Probab. Appl., 38:4 (1993), 660–672
131.
N. S. Bakhvalov, A. A. Borovkov, R. L. Dobrushin, A. V. Zabrodin, V. M. Zolotarev, I. A. Ibragimov, Yu. V. Prokhorov, B. A. Sevast'yanov, Ya. G. Sinai, A. V. Skorokhod, V. A. Statulyavichus, R. Z. Khas'minskii, A. S. Kholevo, D. M. Chibisov, A. N. Shiryaev, “Memorial: Nikolai Nikolaevitch Chentsov”, Theory Probab. Appl., 38:3 (1993), 506–515 (cited: 1)
132.
V. I. Arnol'd, N. S. Bakhvalov, K. V. Brushlinskii, I. M. Gel'fand, R. L. Dobrushin, A. V. Zabrodin, I. A. Ibragimov, S. P. Kurdyumov, S. P. Novikov, D. E. Okhotsimskii, Yu. V. Prokhorov, Yu. B. Radvogin, Ya. G. Sinai, R. Z. Khas'minskii, A. S. Holevo, A. N. Shiryaev, T. M. Eneev, “Nikolai Nikolaevich Chentsov (obituary)”, Russian Math. Surveys, 48:2 (1993), 161–166
1992
133.
A. S. Holevo, “Time-ordered exponentials in quantum stochastic calculus”, Quantum probability & related topics, QP-PQ, VII, World Sci. Publ., River Edge, NJ, 1992, 175–202
134.
A. S. Kholevo, “Kratkii obzor sovremennoi statisticheskoi teorii kvantovogo izmereniya”, Kontseptualnye problemy teorii kvantovogo izmereniya, INION RAN, Moskva, 1992, 19–29
1991
135.
A. S. Holevo, “On the Levy-Khinchine formula in the noncommutative probability theory”, VI Sovetsko-yaponskii simpozium po teorii veroyatnostei i matematicheskoi statistike (Kiev, 5-10 avgusta 1991 g.), MIAN, Institut matematiki AN USSR, 1991, 147
136.
A. S. Holevo, “Statistical inference for quantum processes”, Quantum aspects of optical communications (Paris, 1990), Lecture Notes in Phys., 378, Springer, Berlin, 1991, 127–137 (cited: 21)
137.
A. S. Holevo, “An analog of the Itô decomposition for multiplicative processes with values in a Lie group”, Sankhyā Ser. A, 53:2 (1991), 158–161
138.
A. S. Holevo, “Quantum probability and quantum statistics”, Probability theory – 8, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 83, VINITI, Moscow, 1991, 5–132
1990
139.
L. V. Denisov, A. S. Holevo, “Conditionally positive definite functions on the coefficient algebra of a nonabelian group”, Probability theory and mathematical statistics (Vilnius, 1989), Vol. I, “Mokslas”, Vilnius, 1990, 261–270
140.
A. S. Holevo, “An analog of the Itô decomposition for multiplicative processes with values in a Lie group”, Quantum probability and applications, V (Heidelberg, 1988), Lecture Notes in Math., 1442, Springer, Berlin, 1990, 211–215 (cited: 5)
1989
141.
A. S. Holevo, “Limit theorems for repeated measurements and continuous measurement processes”, Quantum probability and applications, IV (Rome, 1987), Lecture Notes in Math., 1396, Springer, Berlin, 1989, 229–255 (cited: 12)
1991
142.
A. S. Holevo, “Conditionally positive-definite functions in quantum probability theory”, J. Soviet Math., 56:5 (1991), 2670–2697
143.
A. S. Holevo, “A quantum stochastic calculus”, J. Soviet Math., 56:5 (1991), 2609–2624 (cited: 20)
1992
144.
A. S. Holevo, “Stochastic representations of quantum dynamical semi-groups”, Proc. Steklov Inst. Math., 191 (1992), 145–154
1989
145.
A. S. Kholevo, Elementy mnogomernogo sluchainogo analiza i teorii sluchainykh protsessov, MFTI, Moskva, 1989 , 86 pp.
1988
146.
A. S. Kholevo (red.), Kvantovye sluchainye protsessy i otkrytye sistemy, Sb. statei 1982–1984, Matematika. Novoe v zarubezhnoi nauke, 42, Mir, M., 1988 , 223 pp.
147.
A. S. Holevo, “A noncommutative generalization of conditionally positive definite functions”, Quantum probability and applications, III (Oberwolfach, 1987), Lecture Notes in Math., 1303, Springer, Berlin, 1988, 128–148 (cited: 15)
1987
148.
A. S. Holevo, “Conditionally positive definite functions in quantum probability”, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), v. 1, 2, Amer. Math. Soc., Providence, RI, 1987, 1011–1020
149.
A. S. Holevo, “Lévy–Khintchine Representation in Quantum Theory of Probability”, Theory Probab. Appl., 32:1 (1987), 131–136 (cited: 5)
150.
A. S. Holevo, “Quantum estimation”, Adv. Statist. Signal Proc., v. 1, JAI Press Inc., 1987, 157–202
151.
A. S. Kholevo, “On a generalization of canonical quantization”, Math. USSR-Izv., 28:1 (1987), 175–188
152.
A. S. Holevo, “Infinite-divisible instruments in quantum probability theory”, Theory Probab. Appl., 31:3 (1987), 493–497 (cited: 3)
1986
153.
A. S. Kholevo, “Bezgranichno delimye kharakteristicheskie funktsii v kvantovoi teorii veroyatnostei”, Tezisy Vsemirnogo Kongressa Obsch. Bernulli, t.2 (Tashkent, sentyabr 1986 g.), Nauka, Moskva, 1986, 691
1985
154.
A. S. Holevo, “Statistical definition of observable and the structure of statistical models”, Rep. Math. Phys., 22:3 (1985), 385–407 (cited: 15)
155.
A. S. Holevo, Statistical structure of quantum mechanics and hidden parameters, Novoe v Zhizni, Nauke, Tekhnike: Seriya “Matematika, Kibernetika” [Current Life, Science and Technology: Series “Mathematics and Cybernetics”], 85, “Znanie”, Moscow, 1985 , 32 pp.
156.
A. S. Holevo, “On the principle of quantum nondemolition measurements”, Theoret. and Math. Phys., 65:3 (1985), 1250–1255 (cited: 1) (cited: 5)
1984
157.
A. S. Holevo, “Covariant measurements and imprimitivity systems”, Quantum probability and applications to the quantum theory of irreversible processes (Villa Mondragone, 1982), Lecture Notes in Math., 1055, Springer, Berlin, 1984, 153–172 (cited: 31)
158.
A. S. Kholevo, “Nepreryvnye izmereniya nad kvantovym sluchainym protsessom”, Tezisy dokladov 6-go Mezhdunar. Simpoziuma po Teorii Informatsii (Tashkent, 18-22 sentyabrya 1984 g.), AN SSSR, AN UzSSR, 1984, 255–257
1983
159.
A. S. Holevo, “Bounds for generalized uncertainty of the shift parameter”, Probability theory and mathematical statistics (Tbilisi, 1982), Lecture Notes in Math., 1021, Springer, Berlin, 1983, 243–251 (cited: 7)
160.
N. A. Bogomolov, A. S. Kholevo, “A characterization of the covariant resolutions of the identity”, Funct. Anal. Appl., 17:2 (1983), 131–132
161.
A. S. Holevo, “Generalized imprimitivity systems for abelian groups”, Soviet Math. (Iz. VUZ), 27:2 (1983), 53–80
162.
A. S. Holevo, “On measurements of the parameters of a quantum random process”, Theoret. and Math. Phys., 57:3 (1983), 1238–1247
163.
A. S. Kholevo, “Izmereniya parametrov kvantovogo sluchainogo protsessa”, 2-e Vsesoyuznoe soveschanie po Teoretich. Metrologii. Tezisy dokladov (Leningrad, 29-31 marta 1983 g.), GK SSSR po standartam, AN SSSR, 1983, 28–29
1982
164.
A. S. Holevo, “Testing statistical hypotheses in quantum theory”, statya na russkom yazyke (rezyume na angliiskom), Probab. Math. Statist., 3:1 (1982), 113–126 http://www.math.uni.wroc.pl/~pms/files/3.1/Article/3.1.9.pdf (1983)
165.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Translated from the Russian by the author, North-Holland Series in Statistics and Probability, 1, North-Holland Publishing Co., Amsterdam, 1982 , xii+312 pp.
166.
A. S. Holevo, “Quantum-probabilistic investigation of the statistics of readings, using a “Dolinar device””, Soviet Math. (Iz. VUZ), 26:8 (1982), 1–20
167.
A. S. Kholevo, N. A. Bogomolov, “Ob odnoi granitse tochnosti kovariantnykh kvantovykh izmerenii”, Trudy VTs MGU, MGU, 1982, 78–79
168.
A. S. Holevo, “On the structure of generalized imprimitivity systems”, Int. Congress Math., Abstracts, v.XI (Warszawa, August 1983), MIAN, 1982, 53
1981
169.
H. A. Bogomolov, A. S. Kholevo, “Razlozheniya edinitsy, kovariantnye otnositelno predstavleniya abelevoi lokalno kompaktnoi gruppy”, Tr. NIVTs MGU, M., 1981, 45–59
170.
A. S. Kholevo, “Sootnosheniya neopredelennostei dlya uglovogo parametra”, Tezisy 3-i Mezhdunar. konf. po Teorii Veroyat. i Statist., t.2 (Vilnyus, 22-27 iyunya 1981 g.), Institut matematiki i kibernetiki AN LitSSR, 1981, 232–233
1980
171.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Nauka, Moscow, 1980 , 320 pp.
1979
172.
A. S. Holevo, “Covariant measurements and uncertainty relations”, Rep. Math. Phys., 16:3 (1979), 385–400 (cited: 16) (cited: 60)
173.
A. S. Holevo, “On Capacity of a Quantum Communications Channel”, Problems Inform. Transmission, 15:4 (1979), 247–253 (cited: 68)
174.
A. S. Kholevo, “Minimaksnye izmereniya parametrov kvantovogo sostoyaniya”, Tezisy dokladov 5-go Mezhdunar. Simp. po Teorii Informatsii, ch. II (Tbilisi, avgust 1979 g.), Nauchnyi sovet po probleme “KIBERNETIKA” AN SSSR, 1979, 194–196
1978
175.
A. S. Holevo, “Estimation of shift parameters of a quantum state”, Rep. Math. Phys., 13:3 (1978), 379–399 (cited: 42)
1979
176.
N. P. Rasulov, A. S. Holevo, “A regression problem for continuous time series”, Theory Probab. Appl., 22:4 (1979), 731–740 (cited: 1)
177.
A. S. Holevo, “On asymptotically optimal hypotheses testing in quantum statistics”, Theory Probab. Appl., 23:2 (1979), 411–415 (cited: 14)
178.
A. A. Novikov, A. S. Holevo, “The Twelfth All-Union Seminar on Probability Theory and Mathematical Statistics”, Theory Probab. Appl., 23:4 (1979), 853
1977
179.
A. S. Holevo, “Commutation superoperator of a state and its applications to the noncommutative statistics”, Rep. Mathematical Phys., 12:2 (1977), 251–271 (cited: 4)
180.
A. S. Holevo, “Problems in the mathematical theory of quantum communication channels”, Rep. Mathematical Phys., 12:2 (1977), 273–278 (cited: 20) (cited: 51)
1978
181.
A. S. Kholevo, “Investigations in the general theory of statistical decisions”, Proc. Steklov Inst. Math., 124 (1978), 1–140
1976
182.
A. S. Holevo, “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory”, Proceedings of the Third Japan–USSR Symposium on Probability Theory (Tashkent, 1975), Lecture Notes in Math., 550, Springer, Berlin, 1976, 194–222
1981
183.
A. S. Holevo, “An integral over a measure with values in the space conjugated to a partially ordered Banach space”, J. Soviet Math., 16:2 (1981), 934–939
1975
184.
A. S. Holevo, “On a vector-valued integral in the “noncommutative” statistical decision theory”, J. Multivariate Anal., 5:4 (1975), 462–465
185.
A. S. Holevo, “Some statistical problems for quantum Gaussian states”, IEEE Trans. Information Theory, IT-21:5 (1975), 533–543 (cited: 34) (cited: 34)
186.
A. S. Holevo, “Mathematical problems in the theory of quantum channels”, International Conference on Mathematical Problems of Quantum Field Theory and Quantum Statistics. Part I. Axiomatic quantum field theory, Collection of talks (Moscow, 12–17 December, 1972), Trudy Mat. Inst. Steklov., 135, 1975, 226–227
187.
A.S. Kholevo, Issledovaniya po obschei teorii statisticheskikh reshenii, Diss. dokt. fiz.-matem. nauk, MIAN, Moskva, 1975 , 320 pp.
1974
188.
A. S. Kholevo, “The theory of statistical decisions on an operator algebra”, Sov. Math. Dokl., 15 (1974), 1276–1281 (1975)
189.
A. S. Kholevo, “Optimal measurement of the mean value of a Gaussian state”, Engrg. Cybernetics, 12:5 (1974), 128–130
190.
A. S. Holevo, “Remarks on Optimal Quantum Measurements”, Problems Inform. Transmission, 10:4 (1974), 317–320
1973
191.
A. S. Holevo, “On the general problem of mean estimation”, J. Multivariate Anal., 3 (1973), 262–275 (cited: 1)
192.
A. S. Holevo, “Statistical decision theory for quantum systems”, J. Multivariate Anal., 3 (1973), 337–394 (cited: 48) (cited: 316)
193.
A. S. Holevo, “A Generalization of the Rao–Cramér Inequality”, Theory Probab. Appl., 18:2 (1973), 359–362
194.
A. S. Holevo, “Information-Theoretical Aspects of Quantum Measurement”, Problems Inform. Transmission, 9:2 (1973), 110–118
195.
A. S. Holevo, “Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel”, Problems Inform. Transmission, 9:3 (1973), 177–183
196.
A. S. Holevo, “Optimal quantum measurements”, Theoret. and Math. Phys., 17:3 (1973), 1172–1177 (cited: 4)
197.
A. S. Holevo, “On the quasiequivalence of quasifree states on the $C^*$-algebra of CAR”, Theoret. and Math. Phys., 14:2 (1973), 107–111
198.
A. S. Holevo, “Statistical problems in quantum physics”, Proceedings of the Second Japan-USSR Symposium on Probability Theory, Lecture Notes in Math., 330, eds. G. Maruyama, Yu. V. Prokhorov, Springer-Verlag, 1973, 104–119
199.
A. S. Kholevo, “Statisticheskie resheniya v kvantovoi teorii”, Teor. veroyat. i ee primen., 18:2 (1973), 442–444
200.
A. S. Kholevo, “O nekommutativnom analoge metoda maksimalnogo pravdopodobiya”, Tezisy Mezhdunar. konf. po Teorii Veroyat. i Statist., ch.2 (Vilnyus, 25-30 iyunya 1973 g.), AN SSSR, AN LitSSR, 1973, 317–320
201.
A. S. Kholevo, “Optimalnye izmereniya parametrov kvantovykh signalov.”, Tezisy 3-go Mezhdunar. Simp. po Teorii Informatsii, ch.1 (Tallin, 18-23 iyunya 1973 g.), AN SSSR, AN ESSR, 1973, 147–149
1972
202.
A. S. Holevo, “An analogue of statistical decision theory and noncommutative probability theory”, Trudy Moskov. Mat. Obšč., 26, 1972, 133–149
1973
203.
A. S. Kholevo, “On estimating functions of the mean”, Theory Probab. Appl., 17:3 (1973), 543–547
204.
A. S. Kholevo, “Some statistical problems for quantum fields”, Theory Probab. Appl., 17:2 (1973), 347–351
1972
205.
A. S. Holevo, “On the Mathematical Theory of Quantum Communication Channels”, Problems Inform. Transmission, 8:1 (1972), 47–54
206.
A. S. Holevo, “On quasiequivalence of locally normal states”, Theoret. and Math. Phys., 13:2 (1972), 1071–1082 (cited: 11)
207.
A. S. Holevo, “Statistical problems in quantum physics”, Proc. 2nd Japan-USSR Symp. on Probab. Theory, v.1 (Kyoto, 1972), Kyoto University, 1972, 22–40
1971
208.
A. S. Holevo, “Quasifree states of the $C^*$ algebra of CCR. II”, Theoret. and Math. Phys., 6:2 (1971), 103–107 (cited: 2)
209.
A. S. Holevo, “Quasi-free states on the $C^*$ algebra of CCR”, Theoret. and Math. Phys., 6:1 (1971), 1–12 (cited: 3)
210.
A. S. Holevo, “On asymptotic normality of estimates of regression coefficients”, Theory Probab. Appl., 16:4 (1971), 707–711
211.
A. S. Holevo, “On asymptotic efficiency of pseudo-best estimators”, Theory Probab. Appl., 16:3 (1971), 516–527
212.
A. S. Holevo, “Almost periodic signal estimations”, Theory Probab. Appl., 16:2 (1971), 249–263
1970
213.
A. S. Holevo, “Quantum Characteristic Functions”, Problems Inform. Transmission, 6:4 (1970), 316–321
1969
214.
A. S. Holevo, “On estimates of regression coefficients”, Theory Probab. Appl., 4:1 (1969), 79–104
215.
A.S. Kholevo, Ob otsenkakh koeffitsientov regressii, Diss. kand. fiz.-matem. nauk, MIAN, Moskva, 1969 , 73 pp.
1967
216.
A. S. Holevo, “Estimates of the drift parameters for a diffusion process by the method of stochastic approximation”, Studies in the Theory of Self-adjusting Systems, 12, Vyčisl. Centr Akad. Nauk SSSR, Moscow, 1967, 179–200
217.
A. S. Kholevo, “On Sequential Estimates of Parameters”, Theory Probab. Appl., 12:1 (1967), 147–152
1965
218.
A. S. Holevo, “Generalization to spaces with an indefinite metric of a theorem of von Neumann on the operator $T^* T$”, Azerbaĭdžan. Gos. Univ. Učen. Zap. Ser. Fiz.-Mat. Nauk, 1965:2 (1965), 45–48
219.
A. S. Holevo, “Automata which predict a random process”, Soviet Physics Dokl., 10 (1965), 816–818
Generators of quantum 1-dimensional diffusions A. S. Holevo International conference "Quantum information, statistics, probability" with a special session dedicated to A. S. Holevo's 75-th birthday September 13, 2018 10:30
On the 100th anniversary of Claude Shannon A. S. Holevo Seminar of the Department of Probability Theory "Stochastic Analysis: Theory and Applications", Steklov Mathematical Institute of RAS September 8, 2016
О характеризации гауссовских операторов перехода A. S. Holevo Seminar of the Department of Probability Theory "Stochastic Analysis: Theory and Applications", Steklov Mathematical Institute of RAS September 3, 2015 13:00
Quantum channels and their entropic characteristics Alexander Holevo School-Seminar "Interaction of Mathematics and Physics: New Perspectives" for graduate students and young researchers August 27, 2012 15:00
A. S. Holevo, Mathematical foundations of quantum informatics, Lekts. Kursy NOC, 30, 2018, 118 с. http://mi.mathnet.ru/book1730
A. S. Holevo, Investigations in the general theory of statistical decisions, Trudy Mat. Inst. Steklov., 124, ed. S. M. Nikol'skii, 1976, 141 с. http://mi.mathnet.ru/book1300
2019
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