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, “PROBABILITY MEASURES ON THE SET OF QUANTUM STATES
IN OPTIMIZATION PROBLEMS FOR INFORMATION QUANTITIES”, THEORY PROBAB. APPL., 71:2 (2026), 280–290
2.
A. S. Holevo, “Mathematical basics of quantum information science”, Trudy Mat. Inst. Steklova, 2026 (to appear)
3.
A. S. Holevo, A. V. Utkin, “Quantum Accessible Information and Classical Entropy Inequalities”, Lobachevskii Journal of MathematicsVol. , No. 6, pp. 2499–2527, 47:6 (2026), 2499–2527 (to appear), arXiv: 2506.06700
4.
A. S. Holevo, A. V. Utkin, “A conjecture on a tight norm inequality in the finite-dimensional l_p.”, Lobachevskii Journal of Mathematics, 47:7 (2026), 3300–3310 (to appear), arXiv: 2603.24017
2025
5.
D. A. Kronberg, A. S. Kholevo, “Novye podkhody k otsenkam informatsii perekhvatchika v problemakh kvantovoi kriptografii”, Voprosy kiberbezopasnosti, 2025, no. 3 (67), 110-117
6.
A. S. Holevo, “Tight lower bounds for Shannon entropy from ‘quantum pyramids’”, Russian Math. Surveys, 80:4 (2025), 729–731
7.
A. S. Holevo, “Estimating distances between quantum Gaussian states”, Lobachevskii J. Math., 46:6 (2025), 2548–2559
A. V. Bulinski, A. A. Gushchin, M. V. Zhitlukhin, V. V. Kozlov, A. D. Manita, A. A. Muravlev, A. A. Novikov, I. V. Pavlov, D. V. Treschev, A. S. Holevo, E. B. Yarovaya, P. A. Yaskov, “Albert Nikolaevich Shiryaev (on his 90th birthday)”, Russian Math. Surveys, 80:1 (2025), 161–168
2024
9.
A. S. Holevo, “Information capacity of state ensembles and observables”, Lobachevskii J. Math., 45:6 (2024), 2509–2526
2023
10.
Alexander S. Holevo, Sergey N. Filippov, “Quantum Gaussian maximizers and log-Sobolev inequalities”, Lett. Math. Phys., 113 (2023), 10, 23 pp.
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
14.
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
2022
15.
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
16.
A. S. Holevo, “Logarithmic Sobolev inequality and Hypothesis of Quantum Gaussian Maximizers”, Russian Math. Surveys, 77:4 (2022), 766–768
17.
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
18.
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
27.
A. S. Holevo, “Schatten Class Operators in a Representation Space of Canonical Commutation Relations”, Proc. Steklov Inst. Math., 309 (2020), 150–158
28.
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
35.
A. S. Holevo, A. A. Kuznetsova, “Corrigendum: Information capacity of continuous variable measurement channel”, J. Phys. A: Math. Theor., 53 (2020), 459501, 1 pp.
2019
36.
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
37.
A. S. Kholevo, “Generators of quantum one-dimensional diffusions”, Theory Probab. Appl., 64:2 (2019), 249–263
38.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction., 2nd ed., extended and complemented, De Gruyter, Berlin–Boston, 2019, xv+350 pp.
39.
M. E. Shirokov, A. S. Holevo, “Energy-constrained diamond norms and quantum dynamical semigroups”, Lobachevskii J. Math., 40:10 (2019), 1569–1586
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/
2018
41.
Math. Notes, 103:1 (2018), 133–144
42.
A. S. Holevo, “Mathematical foundations of quantum informatics”, Lekts. Kursy NOC, 30, 2018, 3–118
2017
43.
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
2018
44.
A. S. Holevo, “ON THE CLASSICAL CAPACITY OF A CHANNEL WITH STATIONARY QUANTUM GAUSSIAN NOISE”, THEORY PROBAB. APPL., 62:4 (2018), 534–551
2017
45.
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
2017
49.
A. S. Holevo, “On a characterization of Gaussian transition operators”, Theory Probab. Appl., 61:4 (2017), 715–718
2016
50.
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
54.
A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367
55.
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
56.
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)
2014
58.
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
59.
A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14
2015
60.
A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels. II”, Theory Probab. Appl., 59:1 (2015), 145–154
2014
61.
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)
65.
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
67.
A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31
68.
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
69.
A. A. Kuznetsova, A. S. Holevo, “Coding Theorems for Hybrid Channels”, Theory Probab. Appl., 58:2 (2014), 264–285
2013
70.
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
71.
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
2012
72.
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
2011
74.
A. S. Holevo, “Entropy gain and the Choi–Jamiolkowski correspondence for infinite-dimensional quantum evolutions”, Theoret. and Math. Phys., 166:1 (2011), 123–138
75.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, 2nd edition, Edizioni della Normale, Pisa, 2011
76.
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
79.
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
80.
A. S. Holevo, “Statistical inference for quantum systems”, International Encyclopedia of Statistical Science, eds. M. Lovric, Springer, 2011, 1420–1423
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
84.
A. S. Kholevo, “Kvantovaya teoriya informatsii. Kanaly i propusknye sposobnosti”, Informatsionnye tekhnologii i vychislitelnye sistemy, 3 (2010), 39–46
85.
A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218
86.
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, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11
2006
98.
A. S. Holevo, “The additivity problem in quantum information theory”, International Congress of Mathematicians, Vol. III, Eur. Math. Soc., Zürich, 2006, 999–1018
99.
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
2007
102.
A. S. Holevo, “Complementary channels and the additivity problem”, Theory Probab. Appl., 51:1 (2007), 92–100
2006
103.
A. S. Holevo, “Locating a photon:position observables and an uncertainty relation”, Russian Microelectronics, 35:1 (2006), 21–30
104.
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
2005
106.
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
107.
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
108.
A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98
109.
A. S. Holevo, “The additivity problem and constrained quantum channels”, Proc. Int. Soc. Opt. Eng., 5833 (2005), 196–201
110.
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
2004
112.
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
2005
114.
A. S. Holevo, “Asymptotic estimation of a shift parameter of a quantum state”, Theory Probab. Appl., 49:2 (2005), 207–220
2003
115.
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
116.
A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, 2-e izd., Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003, 410 pp.
117.
A. S. Kholevo, Statisticheskaya struktura kvantovoi teorii, Institut kompyuternykh issledovanii, Izhevsk, 2003, 192 pp.
2004
118.
A. S. Holevo, “Entanglement-assisted capacities of constrained quantum channels”, Theory Probab. Appl., 48:2 (2004), 243–255
2003
119.
A. S. Holevo, “Optimal receiver of a binary coherent signals based on the principle of optical feedback”, Laser Physics, 13:12 (2003), 1558–1561
2004
120.
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
121.
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. Kholevo, Vvedenie v kvantovuyu teoriyu informatsii, MTsNMO, M., 2002, 128 pp.
2003
125.
G. G. Amosov, A. S. Holevo, “On the multiplicativity hypothesis for quantum communication channels”, Theory Probab. Appl., 47:1 (2003), 123–127
2002
126.
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
127.
A. S. Holevo, Statistical structure of quantum theory, Lecture Notes in Physics. Monographs, 67, Springer-Verlag, Berlin, 2001, x+159 pp.
A. S. Holevo, “Coding theorems of quantum information theory”, XIIIth International Congress on Mathematical Physics (London, 2000), Int. Press, Boston, MA, 2001, 415–422
129.
A. S. Holevo, “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory”, Math. Methods Statist., 10:1 (2001), 6–22
130.
A. S. Holevo, “An invitation to quantum estimation”, Math. Methods Statist., 10:1 (2001), 1–5
131.
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
2026
