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
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
8.
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
9.
A. S. Holevo, “Logarithmic Sobolev inequality and Hypothesis of Quantum Gaussian Maximizers”, Russian Math. Surveys, 77:4 (2022), 766–768
10.
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
11.
A. S. Holevo, “Quantum noise as noncommutative stationary random process”, Int. J. Mod. Phys. A, 37:20-21 (2022), 22430011 , 15 pp. ;
A. S. Holevo, “On conditions for an operator to be in the class $\mathscr{S}_{p}$”, Russian Math. Surveys, 75:1 (2020), 193–195
18.
A. S. Holevo, “Schatten Class Operators in a Representation Space of Canonical Commutation Relations”, Proc. Steklov Inst. Math., 309 (2020), 150–158
19.
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.
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, “Information Capacities of Noisy Homodyning”, Nanoindustry, 13:4s(99) (2020), 676–677
26.
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
27.
A. S. Kholevo, “Generators of quantum one-dimensional diffusions”, Theory Probab. Appl., 64:2 (2019), 249–263
28.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction., 2nd ed., extended and complemented, De Gruyter, Berlin–Boston, 2019 , xv+350 pp.
29.
M. E. Shirokov, A. S. Holevo, “Energy-constrained diamond norms and quantum dynamical semigroups”, Lobachevskii J. Math., 40:10 (2019), 1569–1586
A. S. Holevo, “Mathematical foundations of quantum informatics”, Lekts. Kursy NOC, 30, 2018, 3–118
32.
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
33.
A. S. Holevo, “ON THE CLASSICAL CAPACITY OF A CHANNEL WITH STATIONARY QUANTUM GAUSSIAN NOISE”, THEORY PROBAB. APPL., 62:4 (2018), 534–551
34.
I. Siemon, A. S. Holevo, R. F. Werner, “Unbounded generators of dynamical semigroups”, Open Syst. Inf. Dyn., 24:4 (2017), 1740015 , 24 pp.
A. S. Holevo, “On the proof of the majorization theorem for quantum Gaussian channels”, Russian Math. Surveys, 71:3 (2016), 585–587
38.
A. S. Holevo, “On a characterization of Gaussian transition operators”, Theory Probab. Appl., 61:4 (2017), 715–718
39.
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
V. Giovannetti, A. S. Holevo, A. Mari, “Majorization and additivity for multimode bosonic Gaussian channels”, Theoret. and Math. Phys., 182:2 (2015), 284–293
42.
A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367
43.
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
44.
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.
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)
46.
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
47.
A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14
48.
A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels. II”, Theory Probab. Appl., 59:1 (2015), 145–154
49.
A. Mari, V. Giovannetti, A. S. Holevo, “Quantum state majorization at the output of bosonic Gaussian channels”, Nature Communications, 5 (2014), 3826 , 5 pp.
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.
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. Holevo, Quantum systems, channels, information. A mathematical introduction, De Gruyter, Berlin–Boston, 2013 , 370 pp. (rasshirennoe i ispravlennoe izdanie angliiskogo perevoda monografii)
53.
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.
A. S. Holevo, “Extreme bosonic linear channels”, Theoret. and Math. Phys., 174:2 (2013), 288–297
55.
A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31
56.
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
57.
A. A. Kuznetsova, A. S. Holevo, “Coding Theorems for Hybrid Channels”, Theory Probab. Appl., 58:2 (2014), 264–285
58.
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
59.
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
60.
A. S. Holevo, V. Giovannetti, “Quantum channels and their entropic characteristics”, Rep. Prog. Phys., 75 (2012), 046001 , 45 pp.
A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10
62.
A. S. Holevo, “Entropy gain and the Choi–Jamiolkowski correspondence for infinite-dimensional quantum evolutions”, Theoret. and Math. Phys., 166:1 (2011), 123–138
63.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, 2nd edition, Edizioni della Normale, Pisa, 2011
64.
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.
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
67.
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. 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, “The entropy gain of infinite-dimensional quantum evolutions”, Dokl. Math., 82:2 (2010), 730–731
71.
A. S. Kholevo, “Kvantovaya teoriya informatsii. Kanaly i propusknye sposobnosti”, Informatsionnye tekhnologii i vychislitelnye sistemy, 3 (2010), 39–46
72.
A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218
73.
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, “Entanglement-Breaking Channels in Infinite Dimensions”, Problems Inform. Transmission, 44:3 (2008), 171–184
80.
M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90
81.
A. S. Holevo, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11
82.
A. S. Holevo, “The additivity problem in quantum information theory”, International Congress of Mathematicians, Vol. III, Eur. Math. Soc., Zürich, 2006, 999–1018
83.
N. Datta, M. Fukuda, A. S. Holevo, “Complementarity and additivity for covariant channels”, Quantum Inf. Process., 5:3 (2006), 179–207
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, “Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory”, Russian Math. Surveys, 61:2 (2006), 301–339
86.
A. S. Holevo, “Complementary channels and the additivity problem”, Theory Probab. Appl., 51:1 (2007), 92–100
87.
A. S. Holevo, “Locating a photon:position observables and an uncertainty relation”, Russian Microelectronics, 35:1 (2006), 21–30
88.
N. Datta, A. S. Holevo, Yu. M. Suhov, “Additivity for transpose depolarizing channels”, Int. J. Quant. Inform.,, 4:1 (2006), 85–98
A. S. Holevo, “Quantum channels: classical capacity”, Encyclopedia of Mathematical Physics, Academic Press, 2006, 142–144
90.
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
91.
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
92.
A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98
93.
A. S. Holevo, “The additivity problem and constrained quantum channels”, Proc. Int. Soc. Opt. Eng., 5833 (2005), 196–201
94.
A. S. Holevo, “Additivity conjecture and covariant channels”, Int. J. Quant., 3:1 (2005), 41–48
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
96.
A. S. Holevo, M. E. Shirokov, “On Shor's channel extension and constrained channels”, Comm. Math. Phys., 249:2 (2004), 417–430
A. S. Holevo, M. E. Shirokov, “The additivity problem for constrained quantum channels”, Russian Math. Surveys, 59:2 (2004), 385–387
98.
A. S. Holevo, “Asymptotic estimation of a shift parameter of a quantum state”, Theory Probab. Appl., 49:2 (2005), 207–220
99.
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
100.
A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, 2-e izd., Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003 , 410 pp.
101.
A. S. Kholevo, Statisticheskaya struktura kvantovoi teorii, Institut kompyuternykh issledovanii, Izhevsk, 2003 , 192 pp.
102.
A. S. Holevo, “Entanglement-assisted capacities of constrained quantum channels”, Theory Probab. Appl., 48:2 (2004), 243–255
103.
A. S. Holevo, “Optimal receiver of a binary coherent signals based on the principle of optical feedback”, Laser Physics, 13:12 (2003), 1558–1561
104.
A. S. Holevo, “On states, channels, and purification”, Quantum Inf. Process., 1:1-2 (2002), 1–4
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, “Coding theorems of quantum information theory”, XIIIth International Congress on Mathematical Physics (London, 2000), Int. Press, Boston, MA, 2001, 415–422
111.
A. S. Holevo, “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory”, Math. Methods Statist., 10:1 (2001), 6–22
112.
A. S. Holevo, “An invitation to quantum estimation”, Math. Methods Statist., 10:1 (2001), 1–5
113.
A. S. Holevo, “Lévy processes and continuous quantum measurements”, Lévy processes, Birkhäuser Boston, Boston, MA, 2001, 225–239
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
116.
A. S. Holevo, M. Sohma, O. Hirota, “Error exponents for quantum channels with constrained inputs”, Rep. Math. Phys., 46:3 (2000), 343–358
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
119.
A. S. Holevo, M. Sohma, O. Hirota, “The capacity of quantum Gaussian channels”, Phys. Rev. A, 59:3 (1999), 1820–1828
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
121.
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
122.
A. S. Holevo, “Covariant quantum dynamical semigroups: unbounded generators”, Irreversibility and causality (Goslar, 1996), Lecture Notes in Phys., 504, Springer, Berlin, 1998, 67–81
A. S. Holevo, “Quantum coding theorems”, Russian Math. Surveys, 53:6 (1998), 1295–1331
126.
M. V. Burnashev, A. S. Holevo, “On the Reliability Function for a Quantum Communication Channel”, Problems Inform. Transmission, 34:2 (1998), 97–107
127.
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
128.
A. S. Holevo, “The structure of classical noise”, Analysis, geometry and probability, Texts Read. Math., 10, Hindustan Book Agency, Delhi, 1996, 73–86
129.
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
130.
A. S. Holevo, “Exponential formulae in quantum stochastic calculus”, Proc. Roy. Soc. Edinburgh Sect. A, 126:2 (1996), 375–389
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
A. S. Holevo, “There exists a non-standard dynamical semigroup on $\mathfrak L(\mathscr H)$”, Russian Math. Surveys, 51:6 (1996), 1206–1207
135.
A. Barchielli, A. S. Holevo, “Constructing quantum measurement processes via classical stochastic calculus”, Stochastic Process. Appl., 58:2 (1995), 293–317
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. Kholevo, “Structure of covariant dynamical semigroups”, Russian Acad. Sci. Dokl. Math., 47:1 (1993), 161–167
142.
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 the Lévy–Khinchin formula in noncommutative probability theory”, Theory Probab. Appl., 38:4 (1993), 660–672
144.
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
145.
A. S. Kholevo, “Kratkii obzor sovremennoi statisticheskoi teorii kvantovogo izmereniya”, Kontseptualnye problemy teorii kvantovogo izmereniya, INION RAN, Moskva, 1992, 19–29
146.
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
147.
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
148.
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
149.
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
150.
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
151.
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, “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, “Conditionally positive-definite functions in quantum probability theory”, J. Soviet Math., 56:5 (1991), 2670–2697
154.
A. S. Holevo, “A quantum stochastic calculus”, J. Soviet Math., 56:5 (1991), 2609–2624
155.
A. S. Holevo, “Stochastic representations of quantum dynamical semi-groups”, Proc. Steklov Inst. Math., 191 (1992), 145–154
156.
A. S. Kholevo, Elementy mnogomernogo sluchainogo analiza i teorii sluchainykh protsessov, MFTI, Moskva, 1989 , 86 pp.
157.
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.
158.
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, “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
160.
A. S. Holevo, “Lévy–Khintchine Representation in Quantum Theory of Probability”, Theory Probab. Appl., 32:1 (1987), 131–136
161.
A. S. Holevo, “Quantum estimation”, Adv. Statist. Signal Proc., v. 1, JAI Press Inc., 1987, 157–202
162.
A. S. Kholevo, “On a generalization of canonical quantization”, Math. USSR-Izv., 28:1 (1987), 175–188
163.
A. S. Holevo, “Infinite-divisible instruments in quantum probability theory”, Theory Probab. Appl., 31:3 (1987), 493–497
164.
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
165.
A. S. Holevo, “Statistical definition of observable and the structure of statistical models”, Rep. Math. Phys., 22:3 (1985), 385–407
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.
167.
A. S. Holevo, “On the principle of quantum nondemolition measurements”, Theoret. and Math. Phys., 65:3 (1985), 1250–1255
168.
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. 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
170.
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
N. A. Bogomolov, A. S. Kholevo, “A characterization of the covariant resolutions of the identity”, Funct. Anal. Appl., 17:2 (1983), 131–132
172.
A. S. Holevo, “Generalized imprimitivity systems for abelian groups”, Soviet Math. (Iz. VUZ), 27:2 (1983), 53–80
173.
A. S. Holevo, “On measurements of the parameters of a quantum random process”, Theoret. and Math. Phys., 57:3 (1983), 1238–1247
174.
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.
177.
A. S. Holevo, “Quantum-probabilistic investigation of the statistics of readings, using a “Dolinar device””, Soviet Math. (Iz. VUZ), 26:8 (1982), 1–20
178.
A. S. Kholevo, N. A. Bogomolov, “Ob odnoi granitse tochnosti kovariantnykh kvantovykh izmerenii”, Trudy VTs MGU, MGU, 1982, 78–79
179.
A. S. Holevo, “On the structure of generalized imprimitivity systems”, Int. Congress Math., Abstracts, v.XI (Warszawa, August 1983), MIAN, 1982, 53
180.
H. A. Bogomolov, A. S. Kholevo, “Razlozheniya edinitsy, kovariantnye otnositelno predstavleniya abelevoi lokalno kompaktnoi gruppy”, Tr. NIVTs MGU, M., 1981, 45–59
181.
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
182.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Nauka, Moscow, 1980 , 320 pp.
183.
A. S. Holevo, “Covariant measurements and uncertainty relations”, Rep. Math. Phys., 16:3 (1979), 385–400
A. S. Holevo, “On Capacity of a Quantum Communications Channel”, Problems Inform. Transmission, 15:4 (1979), 247–253
185.
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
186.
A. S. Holevo, “Estimation of shift parameters of a quantum state”, Rep. Math. Phys., 13:3 (1978), 379–399
N. P. Rasulov, A. S. Holevo, “A regression problem for continuous time series”, Theory Probab. Appl., 22:4 (1979), 731–740
188.
A. S. Holevo, “On asymptotically optimal hypotheses testing in quantum statistics”, Theory Probab. Appl., 23:2 (1979), 411–415
189.
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. Kholevo, “Investigations in the general theory of statistical decisions”, Proc. Steklov Inst. Math., 124 (1978), 1–140
192.
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, “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
194.
A. S. Holevo, “On a vector-valued integral in the “noncommutative” statistical decision theory”, J. Multivariate Anal., 5:4 (1975), 462–465
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
197.
A.S. Kholevo, Issledovaniya po obschei teorii statisticheskikh reshenii, Diss. dokt. fiz.-matem. nauk, MIAN, Moskva, 1975 , 320 pp.
198.
A. S. Kholevo, “The theory of statistical decisions on an operator algebra”, Sov. Math. Dokl., 15 (1974), 1276–1281 (1975)
199.
A. S. Kholevo, “Optimal measurement of the mean value of a Gaussian state”, Engrg. Cybernetics, 12:5 (1974), 128–130
200.
A. S. Holevo, “Remarks on Optimal Quantum Measurements”, Problems Inform. Transmission, 10:4 (1974), 317–320
201.
A. S. Holevo, “On the general problem of mean estimation”, J. Multivariate Anal., 3 (1973), 262–275
A. S. Holevo, “A Generalization of the Rao–Cramér Inequality”, Theory Probab. Appl., 18:2 (1973), 359–362
204.
A. S. Holevo, “Information-Theoretical Aspects of Quantum Measurement”, Problems Inform. Transmission, 9:2 (1973), 110–118
205.
A. S. Holevo, “Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel”, Problems Inform. Transmission, 9:3 (1973), 177–183
206.
A. S. Holevo, “Optimal quantum measurements”, Theoret. and Math. Phys., 17:3 (1973), 1172–1177
207.
A. S. Holevo, “On the quasiequivalence of quasifree states on the $C^*$-algebra of CAR”, Theoret. and Math. Phys., 14:2 (1973), 107–111
208.
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. Kholevo, “Statisticheskie resheniya v kvantovoi teorii”, Teor. veroyat. i ee primen., 18:2 (1973), 442–444
210.
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
211.
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
212.
A. S. Holevo, “An analogue of statistical decision theory and noncommutative probability theory”, Trudy Moskov. Mat. Obšč., 26, 1972, 133–149
213.
A. S. Kholevo, “On estimating functions of the mean”, Theory Probab. Appl., 17:3 (1973), 543–547
214.
A. S. Kholevo, “Some statistical problems for quantum fields”, Theory Probab. Appl., 17:2 (1973), 347–351
215.
A. S. Holevo, “On the Mathematical Theory of Quantum Communication Channels”, Problems Inform. Transmission, 8:1 (1972), 47–54
216.
A. S. Holevo, “On quasiequivalence of locally normal states”, Theoret. and Math. Phys., 13:2 (1972), 1071–1082
217.
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
218.
A. S. Holevo, “Quasifree states of the $C^*$ algebra of CCR. II”, Theoret. and Math. Phys., 6:2 (1971), 103–107
219.
A. S. Holevo, “Quasi-free states on the $C^*$ algebra of CCR”, Theoret. and Math. Phys., 6:1 (1971), 1–12
220.
A. S. Holevo, “On asymptotic normality of estimates of regression coefficients”, Theory Probab. Appl., 16:4 (1971), 707–711
221.
A. S. Holevo, “On asymptotic efficiency of pseudo-best estimators”, Theory Probab. Appl., 16:3 (1971), 516–527
222.
A. S. Holevo, “Almost periodic signal estimations”, Theory Probab. Appl., 16:2 (1971), 249–263
223.
A. S. Holevo, “Quantum Characteristic Functions”, Problems Inform. Transmission, 6:4 (1970), 316–321
224.
A. S. Holevo, “On estimates of regression coefficients”, Theory Probab. Appl., 4:1 (1969), 79–104
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, 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.
234.
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
237.
A. S. Kholevo, “Kvantovaya teoriya informatsii”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 451–453
238.
A. S. Kholevo, K. A. Valiev, “Kvantovyi kompyuter”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 472–473
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
241.
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
242.
M. V. Burnashev, A. S. Holevo, “Letter to the Editor”, Problems Inform. Transmission, 35:1 (1999), 93–94
243.
A. S. Holevo, “International symposium on information theory 1998”, Theory Probab. Appl., 43:4 (1999), 685–686
244.
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
245.
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
246.
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
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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