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. Sber Science Award 2022. 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
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.
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
A. S. Holevo, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11
11.
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.
A. S. Holevo, “Entanglement-Breaking Channels in Infinite Dimensions”, Problems Inform. Transmission, 44:3 (2008), 171–184
13.
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
14.
A. S. Holevo, “On entanglement-assisted classical capacity”, Quantum information theory, J. Math. Phys., 43, no. 9, 2002, 4326–4333
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
A. S. Holevo, “Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel”, Problems Inform. Transmission, 9:3 (1973), 177–183
21.
A. S. Holevo, “Covariant measurements and uncertainty relations”, Rep. Math. Phys., 16:3 (1979), 385–400
A. S. Holevo, “On asymptotically optimal hypotheses testing in quantum statistics”, Theory Probab. Appl., 23:2 (1979), 411–415
23.
A. Barchielli, A. S. Holevo, “Constructing quantum measurement processes via classical stochastic calculus”, Stochastic Process. Appl., 58:2 (1995), 293–317
A. Mari, V. Giovannetti, A. S. Holevo, “Quantum state majorization at the output of bosonic Gaussian channels”, Nature Communications, 5 (2014), 3826 , 5 pp.
A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98
27.
A. S. Holevo, “Problems in the mathematical theory of quantum communication channels”, Rep. Mathematical Phys., 12:2 (1977), 273–278
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
A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10
36.
A. S. Holevo, “Entropy gain and the Choi–Jamiolkowski correspondence for infinite-dimensional quantum evolutions”, Theoret. and Math. Phys., 166:1 (2011), 123–138
37.
A. S. Holevo, “On estimates of regression coefficients”, Theory Probab. Appl., 4:1 (1969), 79–104
38.
V. Giovannetti, A. S. Holevo, A. Mari, “Majorization and additivity for multimode bosonic Gaussian channels”, Theoret. and Math. Phys., 182:2 (2015), 284–293
39.
N. Datta, M. Fukuda, A. S. Holevo, “Complementarity and additivity for covariant channels”, Quantum Inf. Process., 5:3 (2006), 179–207
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
A. S. Holevo, “On translation-covariant quantum Markov equations”, Izv. Math., 59:2 (1995), 427–443
48.
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.
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
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
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.
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.
G. G. Amosov, A. S. Holevo, “On the multiplicativity hypothesis for quantum communication channels”, Theory Probab. Appl., 47:1 (2003), 123–127
61.
A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218
62.
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
63.
A. S. Holevo, M. Sohma, O. Hirota, “Error exponents for quantum channels with constrained inputs”, Rep. Math. Phys., 46:3 (2000), 343–358
A. S. Holevo, “A Generalization of the Rao–Cramér Inequality”, Theory Probab. Appl., 18:2 (1973), 359–362
68.
A. S. Holevo, “Quantum channel capacities”, Quantum Electron., 50:5 (2020), 440–446
69.
A. S. Holevo, “Commutation superoperator of a state and its applications to the noncommutative statistics”, Rep. Mathematical Phys., 12:2 (1977), 251–271
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
A. S. Holevo, “Infinite-divisible instruments in quantum probability theory”, Theory Probab. Appl., 31:3 (1987), 493–497
75.
A. S. Holevo, A. A. Kuznetsova, “Information capacity of continuous variable measurement channel”, J. Phys. A: Math. Theor., 53:17 (2020), 175304 , 13 pp.
Ludovico Lami, Martin B. Plenio, Vittorio Giovannetti, Alexander S. Holevo, “Bosonic Quantum Communication Across Arbitrarily High Loss Channels”, Phys. Rev. Lett., 125:11 (2020), 110504 , 26 pp.
A. S. Holevo, “Extreme bosonic linear channels”, Theoret. and Math. Phys., 174:2 (2013), 288–297
79.
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
A. S. Kholevo, “On a generalization of canonical quantization”, Math. USSR-Izv., 28:1 (1987), 175–188
82.
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
83.
A. S. Holevo, “Excessive maps, “arrival times” and perturbation of dynamical semigroups”, Izv. Math., 59:6 (1995), 1311–1325
84.
A. S. Holevo, “Optimal quantum measurements”, Theoret. and Math. Phys., 17:3 (1973), 1172–1177
85.
A. S. Holevo, “Quasi-free states on the $C^*$ algebra of CCR”, Theoret. and Math. Phys., 6:1 (1971), 1–12
86.
Math. Notes, 103:1 (2018), 133–144
87.
A. S. Holevo, “Exponential formulae in quantum stochastic calculus”, Proc. Roy. Soc. Edinburgh Sect. A, 126:2 (1996), 375–389
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
89.
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
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.
Alexander S. Holevo, Anna A. Kuznetsova, “The information capacity of entanglement-assisted continuous variable quantum measurement”, J. Phys. A, 53:37 (2020), 375307 , 17 pp.
A. S. Holevo, “Asymptotic estimation of a shift parameter of a quantum state”, Theory Probab. Appl., 49:2 (2005), 207–220
98.
A. S. Holevo, “Lévy–Khintchine Representation in Quantum Theory of Probability”, Theory Probab. Appl., 32:1 (1987), 131–136
99.
A. S. Holevo, “On the principle of quantum nondemolition measurements”, Theoret. and Math. Phys., 65:3 (1985), 1250–1255
100.
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
A. S. Holevo, “Structure of a General Quantum Gaussian Observable”, Proc. Steklov Inst. Math., 313 (2021), 70–77
102.
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
103.
A. S. Holevo, “On the proof of the majorization theorem for quantum Gaussian channels”, Russian Math. Surveys, 71:3 (2016), 585–587
104.
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
A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14
117.
A. S. Holevo, “Locating a photon:position observables and an uncertainty relation”, Russian Microelectronics, 35:1 (2006), 21–30
118.
A. S. Holevo, “Stochastic representations of quantum dynamical semi-groups”, Proc. Steklov Inst. Math., 191 (1992), 145–154
119.
A. S. Holevo, “On measurements of the parameters of a quantum random process”, Theoret. and Math. Phys., 57:3 (1983), 1238–1247
120.
A. S. Holevo, “Quasifree states of the $C^*$ algebra of CCR. II”, Theoret. and Math. Phys., 6:2 (1971), 103–107
121.
A. S. Holevo, “Mathematical foundations of quantum informatics”, Lekts. Kursy NOC, 30, 2018, 3–118
122.
A. S. Holevo, “On a characterization of Gaussian transition operators”, Theory Probab. Appl., 61:4 (2017), 715–718
123.
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
124.
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
A. S. Kholevo, “Structure of covariant dynamical semigroups”, Russian Acad. Sci. Dokl. Math., 47:1 (1993), 161–167
127.
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
A. S. Holevo, “On conditions for an operator to be in the class $\mathscr{S}_{p}$”, Russian Math. Surveys, 75:1 (2020), 193–195
137.
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
138.
A. S. Kholevo, “Generators of quantum one-dimensional diffusions”, Theory Probab. Appl., 64:2 (2019), 249–263
139.
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
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
141.
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
A. S. Holevo, “On the quasiequivalence of quasifree states on the $C^*$-algebra of CAR”, Theoret. and Math. Phys., 14:2 (1973), 107–111
148.
A. S. Kholevo, “Some statistical problems for quantum fields”, Theory Probab. Appl., 17:2 (1973), 347–351
149.
A. S. Holevo, On estimates of trace-norm distance between quantum Gaussian states, 2024 , 18 pp., arXiv: 2408.11400
150.
A. S. Holevo, “Information capacity of state ensembles and observables”, Lobachevskii J. Math., 45:6 (2024), 2509–2526;
151.
A. S. Holevo, On estimates of the Bures distance between bosonic Gaussian states, 2024 , 7 pp., arXiv: 2412.04875
152.
A. S. Holevo, “On the Gaussian optimizers hypothesis for bosonic Gaussian channels”, Micro- and Nanoelectronics – 2023: Proc. Internat. Conf. Book of Abstracts (Zvenigorod, Russia, October 2-6, 2023), MAKS Press, 2023, 9
153.
A. S. Holevo, Log-Sobolev inequality and proof of Hypothesis of the Gaussian Maximizers for the capacity of quantum noisy homodyning, 2022 , 19 pp., arXiv: 2204.10626
154.
A. S. Holevo, S. N. Filippov, Proof of the Gaussian maximizers conjecture for the communication capacity of noisy heterodyne measurements, 2022 , 18 pp., arXiv: 2206.02133
155.
A. S. Holevo, “Schatten Class Operators in a Representation Space of Canonical Commutation Relations”, Proc. Steklov Inst. Math., 309 (2020), 150–158
156.
A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, Novoe izd., MTsNMO, 2020 , 363 pp.
157.
A. S. Holevo, “Information Capacities of Noisy Homodyning”, Nanoindustry, 13:4s(99) (2020), 676–677
158.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction., 2nd ed., extended and complemented, De Gruyter, Berlin–Boston, 2019 , xv+350 pp.
159.
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)
160.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction, De Gruyter, Berlin–Boston, 2013 , 370 pp. (rasshirennoe i ispravlennoe izdanie angliiskogo perevoda monografii)
161.
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
162.
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
163.
Yu. I. Bogdanov, N. A. Bogdanova, V. F. Lukichev, A. A. Orlikovsky, I. A. Semenikhin, A. S. Holevo, A. Yu. Chernyavskiy, “Numerical tasks of quantum computer circuits modeling”, Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2013, no. 3, 3–15
164.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, 2nd edition, Edizioni della Normale, Pisa, 2011
165.
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
166.
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
A. S. Kholevo, “Kvantovaya teoriya informatsii. Kanaly i propusknye sposobnosti”, Informatsionnye tekhnologii i vychislitelnye sistemy, 3 (2010), 39–46
169.
T. Heinosaari, A. S. Holevo, M. M. Wolf, “The semigroup structure of Gaussian channels”, Quantum Inf. Comput., 10:7-8 (2010), 619–635
170.
A. S. Holevo, “Quantum information theory. Channels and capacities”, Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2010, no. 3, 39–46
171.
A. S. Holevo, “The additivity problem in quantum information theory”, International Congress of Mathematicians, Vol. III, Eur. Math. Soc., Zürich, 2006, 999–1018
172.
A. S. Holevo, “Quantum channels: classical capacity”, Encyclopedia of Mathematical Physics, Academic Press, 2006, 142–144
173.
A. S. Holevo, “The additivity problem and constrained quantum channels”, Proc. Int. Soc. Opt. Eng., 5833 (2005), 196–201
174.
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
175.
A. S. Holevo, M. E. Shirokov, “The additivity problem for constrained quantum channels”, Russian Math. Surveys, 59:2 (2004), 385–387
176.
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
177.
A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, 2-e izd., Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003 , 410 pp.
178.
A. S. Kholevo, Statisticheskaya struktura kvantovoi teorii, Institut kompyuternykh issledovanii, Izhevsk, 2003 , 192 pp.
179.
A. S. Holevo, “Optimal receiver of a binary coherent signals based on the principle of optical feedback”, Laser Physics, 13:12 (2003), 1558–1561
180.
A. S. Kholevo, Vvedenie v kvantovuyu teoriyu informatsii, MTsNMO, M., 2002 , 128 pp.
181.
A. S. Holevo, “Coding theorems of quantum information theory”, XIIIth International Congress on Mathematical Physics (London, 2000), Int. Press, Boston, MA, 2001, 415–422
182.
A. S. Holevo, “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory”, Math. Methods Statist., 10:1 (2001), 6–22
183.
A. S. Holevo, “An invitation to quantum estimation”, Math. Methods Statist., 10:1 (2001), 1–5
184.
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
185.
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
186.
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
187.
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
188.
A. S. Holevo, “The structure of classical noise”, Analysis, geometry and probability, Texts Read. Math., 10, Hindustan Book Agency, Delhi, 1996, 73–86
189.
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
190.
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
191.
A. S. Kholevo, “Kratkii obzor sovremennoi statisticheskoi teorii kvantovogo izmereniya”, Kontseptualnye problemy teorii kvantovogo izmereniya, INION RAN, Moskva, 1992, 19–29
192.
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
193.
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
194.
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
195.
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
196.
A. S. Kholevo, Elementy mnogomernogo sluchainogo analiza i teorii sluchainykh protsessov, MFTI, Moskva, 1989 , 86 pp.
197.
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.
198.
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
199.
A. S. Holevo, “Quantum estimation”, Adv. Statist. Signal Proc., v. 1, JAI Press Inc., 1987, 157–202
200.
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
201.
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.
202.
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
203.
N. A. Bogomolov, A. S. Kholevo, “A characterization of the covariant resolutions of the identity”, Funct. Anal. Appl., 17:2 (1983), 131–132
204.
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
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.
207.
A. S. Kholevo, N. A. Bogomolov, “Ob odnoi granitse tochnosti kovariantnykh kvantovykh izmerenii”, Trudy VTs MGU, MGU, 1982, 78–79
208.
A. S. Holevo, “On the structure of generalized imprimitivity systems”, Int. Congress Math., Abstracts, v.XI (Warszawa, August 1983), MIAN, 1982, 53
209.
H. A. Bogomolov, A. S. Kholevo, “Razlozheniya edinitsy, kovariantnye otnositelno predstavleniya abelevoi lokalno kompaktnoi gruppy”, Tr. NIVTs MGU, M., 1981, 45–59
210.
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
211.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Nauka, Moscow, 1980 , 320 pp.
212.
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
213.
A. S. Kholevo, “Investigations in the general theory of statistical decisions”, Proc. Steklov Inst. Math., 124 (1978), 1–140
214.
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
215.
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
216.
A.S. Kholevo, Issledovaniya po obschei teorii statisticheskikh reshenii, Diss. dokt. fiz.-matem. nauk, MIAN, Moskva, 1975 , 320 pp.
217.
A. S. Kholevo, “The theory of statistical decisions on an operator algebra”, Sov. Math. Dokl., 15 (1974), 1276–1281 (1975)
218.
A. S. Kholevo, “Optimal measurement of the mean value of a Gaussian state”, Engrg. Cybernetics, 12:5 (1974), 128–130
219.
A. S. Kholevo, “Statisticheskie resheniya v kvantovoi teorii”, Teor. veroyat. i ee primen., 18:2 (1973), 442–444
220.
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
221.
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
222.
A. S. Holevo, “An analogue of statistical decision theory and noncommutative probability theory”, Trudy Moskov. Mat. Obšč., 26, 1972, 133–149
223.
A. S. Kholevo, “On estimating functions of the mean”, Theory Probab. Appl., 17:3 (1973), 543–547
224.
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
225.
A.S. Kholevo, Ob otsenkakh koeffitsientov regressii, Diss. kand. fiz.-matem. nauk, MIAN, Moskva, 1969 , 73 pp.
226.
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
227.
A. S. Kholevo, “On Sequential Estimates of Parameters”, Theory Probab. Appl., 12:1 (1967), 147–152
228.
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
229.
A. S. Holevo, “Automata which predict a random process”, Soviet Physics Dokl., 10 (1965), 816–818
230.
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
231.
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
232.
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
233.
A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583
A. S. Holevo, A. A. Kuznetsova, “Corrigendum: Information capacity of continuous variable measurement channel”, J. Phys. A: Math. Theor., 53 (2020), 459501 , 1 pp.
237.
A. S. Kholevo, “Kvantovaya informatika”, Matematicheskaya sostavlyayuschaya, 2-e izd., rassh. i dop., eds. N. N. Andreev, S. P. Konovalov, N. M. Panyunin, Matematicheskie etyudy, M., 2019, 38https://book.etudes.ru/toc/quantum/
A. S. Holevo, “Statistical inference for quantum systems”, International Encyclopedia of Statistical Science, eds. M. Lovric, Springer, 2011, 1420–1423
240.
A. S. Kholevo, “Kvantovaya teoriya informatsii”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 451–453
241.
A. S. Kholevo, K. A. Valiev, “Kvantovyi kompyuter”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 472–473
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
244.
M. V. Burnashev, A. S. Holevo, “Letter to the Editor”, Problems Inform. Transmission, 35:1 (1999), 93–94
245.
A. S. Holevo, “International symposium on information theory 1998”, Theory Probab. Appl., 43:4 (1999), 685–686
246.
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
247.
A. A. Novikov, A. S. Holevo, “The Twelfth All-Union Seminar on Probability Theory and Mathematical Statistics”, Theory Probab. Appl., 23:4 (1979), 853
Квантовые гауссовские наблюдаемые A. S. Holevo International conference
“Theory of Functions, Operator Theory and Quantum Information Theory” June 8, 2024 12:45
Multiplication formulas for Gaussian operators A. S. Holevo III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 6, 2023 10:00
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
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