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 170 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; International «Quantum Communication Award» — 1996; A. von Humboldt Research Award — 1999. 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
Yu. I. Bogdanov, B. I. Bantysh, V. F. Lukichëv, A. A. Orlikovskii, A. S. Kholevo, “Dinamika stseplennosti v kvantovykh operatsiyakh na sverkhprovodnikovykh fazovykh kubitakh”, Izv. RAN. Ser. fizicheskaya, 78:1 (2014), 13–17
2.
A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14
3.
A. A. Kuznetsova, A. S. Kholevo, “Teoremy kodirovaniya dlya gibridnykh kanalov. II”, TVP, 59:1 (2014), 168–178
4.
A. Mari, V. Giovannetti, A. S. Holevo, “Quantum state majorization at the output of bosonic Gaussian channels”, Nature Communications, 5 (2014), 3826, 5 pp.
5.
V. Giovannetti, A. S. Holevo, A. Mari, Majorization and additivity for multimode bosonic Gaussian channels, 2014, 15 pp., arXiv: 1405.4066
6.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction, De Gruyter, Berlin–Boston, 2013, ISBN: 978-3-11-027325-0, 370 pp. (rasshirennoe i ispravlennoe izdanie angliiskogo perevoda monografii)
7.
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.
8.
A. S. Holevo, “Extreme bosonic linear channels”, Theoret. and Math. Phys., 174:2 (2013), 288–297
9.
A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31
10.
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
11.
A. A. Kuznetsova, A. S. Kholevo, “Coding Theorems for Hybrid Channels”, TVP, 58:2 (2013), 298–324; A. A. Kuznetsova, A. S. Holevo, “Coding Theorems for Hybrid Channels”, Theory Probab. Appl., 58:2 (2014), 264–285
12.
V. Giovannetti, A. S. Holevo, R. Garcia-Patron, A solution of the Gaussian optimizer conjecture, 2013, arXiv: 1312.2251
13.
V. Giovannetti, R. Garcia-Patron, N. J. Cerf, A. S. Holevo, Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture, 2013, arXiv: 1312.6225
14.
A. S. Holevo, V. Giovannetti, “Quantum channels and their entropic characteristics”, Rep. Prog. Phys., 75 (2012), 046001, 45 pp.
15.
A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10
16.
A. S. Holevo, “Entropy gain and the Choi–Jamiolkowski correspondence for infinite-dimensional quantum evolutions”, Theoret. and Math. Phys., 166:1 (2011), 123–138
17.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, 2nd edition, Edizioni della Normale, Pisa, 2011, ISBN: 978-88-7642-375-8
18.
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.
19.
A. S. Holevo, “The Choi-Jamiolkowski forms of quantum Gaussian channels”, J. Math. Phys., 52 (2011), 042202, 12 pp.
20.
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
21.
A. S. Kholevo, Kvantovye sistemy, kanaly, informatsiya, MTsNMO, M., 2010, ISBN: 978-5-94057-574-0, 328 pp.
22.
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
23.
A. S. Holevo, “The entropy gain of infinite-dimensional quantum evolutions”, Dokl. Math., 82:2 (2010), 730–731
24.
A. S. Kholevo, “Kvantovaya teoriya informatsii. Kanaly i propusknye sposobnosti”, Informatsionnye tekhnologii i vychislitelnye sistemy, 3 (2010), 39–46
25.
A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218
26.
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.
27.
T. Heinosaari, A. S. Holevo, M. M. Wolf, “The semigroup structure of Gaussian channels”, Quantum Inf. Comput., 10:7-8 (2010), 619–635
28.
A. S. Holevo, J.-P. Pellonpää, “Extreme Covariant Observables for Type I Symmetry Groups”, Found. Phys., 39:6 (2009), 625–641
29.
F. Caruso, J. Eisert, V. Giovannetti, A. S. Holevo, “Multi-mode bosonic Gaussian channels”, New J. Phys., 10 (2008), 083030, 33 pp.
30.
A. S. Holevo, V. Giovannetti, “Quantum shared broadcasting”, Quantum Inf. Process., 7:2-3 (2008), 55–69
31.
A. S. Holevo, “Entanglement-Breaking Channels in Infinite Dimensions”, Problems Inform. Transmission, 44:3 (2008), 171–184
32.
M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90
33.
A. S. Holevo, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11
34.
A. S. Holevo, “The additivity problem in quantum information theory”, International Congress of Mathematicians, Vol. III, Eur. Math. Soc., Zürich, 2006, 999–1018
35.
N. Datta, M. Fukuda, A. S. Holevo, “Complementarity and additivity for covariant channels”, Quantum Inf. Process., 5:3 (2006), 179–207
36.
F. Caruso, V. Giovannetti, A. S. Holevo, “One-mode Bosonic Gaussian channels: a full weak-degradability classification”, New Journal of Physics, 8 (2006), 310
37.
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
38.
A. S. Kholevo, “Complementary channels and the additivity problem”, TVP, 51:1 (2006), 133–143; A. S. Holevo, “Complementary channels and the additivity problem”, Theory Probab. Appl., 51:1 (2007), 92–100
39.
A. S. Holevo, “Locating a photon:position observables and an uncertainty relation”, Russian Microelectronics, 35:1 (2006), 21–30
40.
N. Datta, A. S. Holevo, Yu. M. Suhov, “Additivity for transpose depolarizing channels”, Int. J. Quant. Inform.,, 4:1 (2006), 85–98
41.
A. S. Holevo, “Quantum channels: classical capacity”, Encyclopedia of Mathematical Physics, Academic Press, 2006, 142–144
42.
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
43.
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
44.
A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98
45.
A. S. Holevo, “The additivity problem and constrained quantum channels”, Proc. Int. Soc. Opt. Eng., 5833 (2005), 196-201
46.
A. S. Holevo, “Additivity conjecture and covariant channels”, Int. J. Quant., 3:1 (2005), 41-48
47.
A. S. Holevo, M. E. Shirokov, “On Shor's channel extension and constrained channels”, Comm. Math. Phys., 249:2 (2004), 417–430
48.
A. S. Holevo, M. E. Shirokov, “The additivity problem for constrained quantum channels”, Russian Math. Surveys, 59:2 (2004), 385–387
49.
A. S. Kholevo, “Asymptotic estimation of a shift parameter of a quantum state”, TVP, 49:2 (2004), 335–350; A. S. Holevo, “Asymptotic estimation of a shift parameter of a quantum state”, Theory Probab. Appl., 49:2 (2005), 207–220
50.
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
51.
A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, 2-e izd., Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003, ISBN: 5939722547, 410 pp.
52.
A. S. Kholevo, Statisticheskaya struktura kvantovoi teorii, Institut kompyuternykh issledovanii, Izhevsk, 2003
53.
A. S. Kholevo, “Entanglement-assisted capacities of constrained quantum channels”, TVP, 48:2 (2003), 359–374; A. S. Holevo, “Entanglement-assisted capacities of constrained quantum channels”, Theory Probab. Appl., 48:2 (2004), 243–255
54.
A. S. Holevo, “Optimal receiver of a binary coherent signals based on the principle of optical feedback”, Laser Physics, 13:12 (2003), 1558–1561
55.
A. S. Holevo, “On states, channels, and purification”, Quantum Inf. Process., 1:1-2 (2002), 1–4
56.
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
57.
A. S. Holevo, “On entanglement-assisted classical capacity”, Quantum information theory, J. Math. Phys., 43, no. 9, 2002, 4326–4333
58.
A. S. Kholevo, Vvedenie v kvantovuyu teoriyu informatsii, MTsNMO, M., 2002, ISBN: 5-94057-017-8, 128 pp.
59.
G. G. Amosov, A. S. Kholevo, “On the multiplicativity hypothesis for quantum communication channels”, TVP, 47:1 (2002), 143–146; G. G. Amosov, A. S. Holevo, “On the multiplicativity hypothesis for quantum communication channels”, Theory Probab. Appl., 47:1 (2003), 123–127
60.
A. S. Holevo, Statistical structure of quantum theory, Lecture Notes in Physics. Monographs, 67, Springer-Verlag, Berlin, 2001, ISBN: 3-540-42082-7, x+159 pp.
61.
A. S. Holevo, “Coding theorems of quantum information theory”, XIIIth International Congress on Mathematical Physics (London, 2000), Int. Press, Boston, MA, 2001, 415–422
62.
A. S. Holevo, “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory”, Math. Methods Statist., 10:1 (2001), 6–22
63.
A. S. Holevo, “An invitation to quantum estimation”, Math. Methods Statist., 10:1 (2001), 1–5
64.
A. S. Holevo, “Lévy processes and continuous quantum measurements”, Lévy processes, Birkhäuser Boston, Boston, MA, 2001, 225–239
65.
A. S. Holevo, R. F. Werner, “Evaluating capacities of Bosonic Gaussian channels”, Phys. Rev. A, 63 (2001), 032312, 13 pp.
66.
A. S. Holevo, M. Sohma, O. Hirota, “Error exponents for quantum channels with constrained inputs”, Rep. Math. Phys., 46:3 (2000), 343–358
67.
A. S. Holevo, “Reliability function of general classical-quantum channel”, IEEE Trans. Inform. Theory, 46:6 (2000), 2256–2261
68.
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
69.
A. S. Holevo, M. Sohma, O. Hirota, “The capacity of quantum Gaussian channels”, Phys. Rev. A, 59:3 (1999), 1820–1828
70.
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
71.
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
72.
A. S. Holevo, “Covariant quantum dynamical semigroups: unbounded generators”, Irreversibility and causality (Goslar, 1996), Lecture Notes in Phys., 504, Springer, Berlin, 1998, 67–81
73.
A. S. Holevo, “Radon-Nikodým derivatives of quantum instruments”, J. Math. Phys., 39:3 (1998), 1373–1387
74.
A. S. Holevo, “The capacity of the quantum channel with general signal states”, IEEE Trans. Inform. Theory, 44:1 (1998), 269–273
75.
A. S. Holevo, “Quantum coding theorems”, Russian Math. Surveys, 53:6 (1998), 1295–1331
76.
M. V. Burnashev, A. S. Holevo, “On the Reliability Function for a Quantum Communication Channel”, Problems Inform. Transmission, 34:2 (1998), 97–107
77.
M. V. Burnashev, A. S. Holevo, On reliability function of quantum communication channel, 1997, 8 pp., arXiv: quant-ph/9703013
78.
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
79.
A. S. Holevo, “The structure of classical noise”, Analysis, geometry and probability, Texts Read. Math., 10, Hindustan Book Agency, Delhi, 1996, 73–86
80.
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
81.
A. S. Holevo, “Exponential formulae in quantum stochastic calculus”, Proc. Roy. Soc. Edinburgh Sect. A, 126:2 (1996), 375–389
82.
A. S. Holevo, “On dissipative stochastic equations in a Hilbert space”, Probab. Theory Related Fields, 104:4 (1996), 483–500
83.
A. S. Holevo, “Covariant quantum Markovian evolutions”, J. Math. Phys., 37:4 (1996), 1812–1832
84.
A. S. Holevo, “There exists a non-standard dynamical semigroup on $\mathfrak L(\mathscr H)$”, Russian Math. Surveys, 51:6 (1996), 1206–1207
85.
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
86.
A. Barchielli, A. S. Holevo, “Constructing quantum measurement processes via classical stochastic calculus”, Stochastic Process. Appl., 58:2 (1995), 293–317
87.
A. S. Holevo, “On the structure of covariant dynamical semigroups”, J. Funct. Anal., 131:2 (1995), 255–278
88.
A. S. Holevo, “On translation-covariant quantum Markov equations”, Izv. Math., 59:2 (1995), 427–443
89.
A. S. Holevo, “Excessive maps, “arrival times” and perturbation of dynamical semigroups”, Izv. Math., 59:6 (1995), 1311–1325
90.
A. S. Holevo, “A note on covariant dynamical semigroups”, Rep. Math. Phys., 32:2 (1993), 211–216
91.
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
92.
A. S. Kholevo, “Structure of covariant dynamical semigroups”, Russian Acad. Sci. Dokl. Math., 47:1 (1993), 161–167
93.
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
94.
A. S. Kholevo, “On the Lévy–Khinchin formula in noncommutative probability theory”, Theory Probab. Appl., 38:4 (1993), 660–672
95.
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
96.
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
97.
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
98.
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
99.
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
100.
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
101.
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
102.
A. S. Kholevo, “Conditionally positive-definite functions in quantum probability theory”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Nov. dostizh., 36, VINITI, M., 1989, 103–147; A. S. Holevo, “Conditionally positive-definite functions in quantum probability theory”, J. Soviet Math., 56:5 (1991), 2670–2697
103.
A. S. Kholevo, “A quantum stochastic calculus”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Nov. dostizh., 36, VINITI, M., 1989, 3–28; A. S. Holevo, “A quantum stochastic calculus”, J. Soviet Math., 56:5 (1991), 2609–2624
104.
A. S. Kholevo, “Stochastic representations of quantum dynamical semi-groups”, Statisticheskaya mekhanika i teoriya dinamicheskikh sistem, K 80-letiyu so dnya rozhdeniya akademika Nikolaya Nikolaevicha Bogolyubova, Tr. MIAN SSSR, 191, Nauka, M., 1989, 130–139; A. S. Holevo, “Stochastic representations of quantum dynamical semi-groups”, Proc. Steklov Inst. Math., 191 (1992), 145–154
105.
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.
106.
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
107.
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
108.
A. S. Holevo, “Lévy–Khintchine Representation in Quantum Theory of Probability”, Theory Probab. Appl., 32:1 (1987), 131–136
109.
A. S. Holevo, “Quantum estimation”, Adv. Statist. Signal Proc., v. 1, JAI Press Inc., 1987, 157–202
110.
A. S. Kholevo, “On a generalization of canonical quantization”, Izv. AN SSSR. Ser. matem., 50:1 (1986), 181–194; A. S. Kholevo, “On a generalization of canonical quantization”, Math. USSR-Izv., 28:1 (1987), 175–188
111.
A. S. Kholevo, “Infinite-divisible instruments in quantum probability theory”, TVP, 31:3 (1986), 560–564; A. S. Holevo, “Infinite-divisible instruments in quantum probability theory”, Theory Probab. Appl., 31:3 (1987), 493–497
112.
A. S. Holevo, “Statistical definition of observable and the structure of statistical models”, Rep. Math. Phys., 22:3 (1985), 385–407
113.
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.
114.
A. S. Holevo, “On the principle of quantum nondemolition measurements”, Theoret. and Math. Phys., 65:3 (1985), 1250–1255
115.
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
116.
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
117.
N. A. Bogomolov, A. S. Kholevo, “A characterization of the covariant resolutions of the identity”, Funct. Anal. Appl., 17:2 (1983), 131–132
118.
A. S. Holevo, “Generalized imprimitivity systems for abelian groups”, Soviet Math. (Iz. VUZ), 27:2 (1983), 53–80
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, “Testing statistical hypotheses in quantum theory”, Probab. Math. Statist., 3:1 (1982), 113–126 (1983)
121.
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, ISBN: 0-444-86333-8, xii+312 pp.
122.
A. S. Holevo, “Quantum-probabilistic investigation of the statistics of readings, using a “Dolinar device””, Soviet Math. (Iz. VUZ), 26:8 (1982), 1–20
123.
H. A. Bogomolov, A. S. Kholevo, “Razlozheniya edinitsy, kovariantnye otnositelno predstavleniya abelevoi lokalno kompaktnoi gruppy”, Tr. NIVTs MGU, M., 1981, 45–59
124.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Nauka, Moscow, 1980, 320 pp.
125.
A. S. Holevo, “Covariant measurements and uncertainty relations”, Rep. Math. Phys., 16:3 (1979), 385–400
126.
A. S. Holevo, “On Capacity of a Quantum Communications Channel”, Problems Inform. Transmission, 15:4 (1979), 247–253
127.
A. S. Holevo, “Estimation of shift parameters of a quantum state”, Rep. Math. Phys., 13:3 (1978), 379–399
128.
N. P. Rasulov, A. S. Kholevo, “A regression problem for continuous time series”, TVP, 23:4 (1978), 762–771; N. P. Rasulov, A. S. Holevo, “A regression problem for continuous time series”, Theory Probab. Appl., 22:4 (1979), 731–740
129.
A. S. Kholevo, “On asymptotically optimal hypotheses testing in quantum statistics”, TVP, 23:2 (1978), 429–432; A. S. Holevo, “On asymptotically optimal hypotheses testing in quantum statistics”, Theory Probab. Appl., 23:2 (1979), 411–415
130.
A. S. Holevo, “Commutation superoperator of a state and its applications to the noncommutative statistics”, Rep. Mathematical Phys., 12:2 (1977), 251–271
131.
A. S. Holevo, “Problems in the mathematical theory of quantum communication channels”, Rep. Mathematical Phys., 12:2 (1977), 273–278
132.
A. S. Kholevo, “Investigations in the general theory of statistical decisions”, Tr. MIAN SSSR, 124, 1976, 3–140, 141 pp. ; A. S. Kholevo, “Investigations in the general theory of statistical decisions”, Proc. Steklov Inst. Math., 124 (1978), 1–140
133.
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
134.
A. S. Kholevo, “Optimalnoe izmerenie amplitud kompleksnykh signalov na fone kvantovogo shuma”, Trudy 4-go Mezhdunarodnogo simpoziuma po teorii informatsii, Leningrad, 1976
135.
A. S. Kholevo, “An integral over a measure with values in the space conjugated to a partially ordered Banach space”, Problemy teorii veroyatnostnykh raspredelenii. 3, Zap. nauchn. sem. LOMI, 55, Izd-vo «Nauka», Leningrad. otd., L., 1976, 26–34; 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
136.
A. S. Holevo, “On a vector-valued integral in the “noncommutative” statistical decision theory”, J. Multivariate Anal., 5:4 (1975), 462–465
137.
A. S. Holevo, “Some statistical problems for quantum Gaussian states”, IEEE Trans. Information Theory, IT-21:5 (1975), 533–543
138.
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
139.
A. S. Kholevo, “The theory of statistical decisions on an operator algebra”, Sov. Math. Dokl., 15 (1974), 1276–1281 (1975)
140.
A. S. Kholevo, “Optimal measurement of the mean value of a Gaussian state”, Engrg. Cybernetics, 12:5 (1974), 128–130
141.
A. S. Holevo, “Remarks on Optimal Quantum Measurements”, Problems Inform. Transmission, 10:4 (1974), 317–320
142.
A. S. Holevo, “On the general problem of mean estimation”, J. Multivariate Anal., 3 (1973), 262–275
143.
A. S. Holevo, “Statistical decision theory for quantum systems”, J. Multivariate Anal., 3 (1973), 337–394
144.
A. S. Holevo, “A Generalization of the Rao–Cramér Inequality”, Theory Probab. Appl., 18:2 (1973), 359–362
145.
A. S. Holevo, “Information-Theoretical Aspects of Quantum Measurement”, Problems Inform. Transmission, 9:2 (1973), 110–118
146.
A. S. Holevo, “Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel”, Problems Inform. Transmission, 9:3 (1973), 177–183
147.
A. S. Holevo, “Optimal quantum measurements”, Theoret. and Math. Phys., 17:3 (1973), 1172–1177
148.
A. S. Holevo, “On the quasiequivalence of quasifree states on the $C^*$-algebra of CAR”, Theoret. and Math. Phys., 14:2 (1973), 107–111
149.
A. S. Holevo, “Statistical problems in quantum physics”, Proceedings of the Second Japan-USSR Symposium on Probability Theory (Kyoto, 1972), Lecture Notes in Math., 330, eds. G. Maruyama, Yu. V. Prokhorov, Springer-Verlag, 1973, 104–119
150.
A. S. Holevo, “An analogue of statistical decision theory and noncommutative probability theory”, Trudy Moskov. Mat. Obšč., 26, 1972, 133–149
151.
A. S. Kholevo, “On estimating functions of the mean”, TVP, 17:3 (1972), 573–577; A. S. Kholevo, “On estimating functions of the mean”, Theory Probab. Appl., 17:3 (1973), 543–547
152.
A. S. Kholevo, “Some statistical problems for quantum fields”, TVP, 17:2 (1972), 360–365; A. S. Kholevo, “Some statistical problems for quantum fields”, Theory Probab. Appl., 17:2 (1973), 347–351
153.
A. S. Holevo, “On the Mathematical Theory of Quantum Communication Channels”, Problems Inform. Transmission, 8:1 (1972), 47–54
154.
A. S. Holevo, “On quasiequivalence of locally normal states”, Theoret. and Math. Phys., 13:2 (1972), 1071–1082
155.
A. S. Holevo, “Quasifree states of the $C^*$ algebra of CCR. II”, Theoret. and Math. Phys., 6:2 (1971), 103–107
156.
A. S. Holevo, “Quasi-free states on the $C^*$ algebra of CCR”, Theoret. and Math. Phys., 6:1 (1971), 1–12
157.
A. S. Holevo, “On asymptotic normality of estimates of regression coefficients”, Theory Probab. Appl., 16:4 (1971), 707–711
158.
A. S. Holevo, “On asymptotic efficiency of pseudo-best estimators”, Theory Probab. Appl., 16:3 (1971), 516–527
159.
A. S. Holevo, “Almost periodic signal estimations”, Theory Probab. Appl., 16:2 (1971), 249–263
160.
A. S. Holevo, “Quantum Characteristic Functions”, Problems Inform. Transmission, 6:4 (1970), 316–321
161.
A. S. Holevo, “On estimates of regression coefficients”, Theory Probab. Appl., 4:1 (1969), 79–104
162.
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
163.
A. S. Kholevo, “On Sequential Estimates of Parameters”, Theory Probab. Appl., 12:1 (1967), 147–152
164.
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
165.
A. S. Holevo, “Automata which predict a random process”, Soviet Physics Dokl., 10 (1965), 816–818
166.
A. S. Holevo, “Statistical inference for quantum systems”, International Encyclopedia of Statistical Science, eds. M. Lovric, Springer, 2011, 1420–1423
167.
A. S. Kholevo, “Kvantovaya teoriya informatsii”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 451–453
168.
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. Kholevo, D. M. Chibisov, A. N. Shiryaev, “On the 80th Birthday of B. A. Sevastyanov”, TVP, 48:4 (2003), 785; 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
171.
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
172.
M. V. Burnashev, A. S. Holevo, “Letter to the Editor”, Problems Inform. Transmission, 35:1 (1999), 93–94
173.
A. S. Kholevo, “International symposium on information theory 1998”, TVP, 43:4 (1998), 823–824; A. S. Holevo, “International symposium on information theory 1998”, Theory Probab. Appl., 43:4 (1999), 685–686
174.
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
175.
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
176.
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
177.
A. A. Novikov, A. S. Kholevo, “The Twelfth All-Union Seminar on Probability Theory and Mathematical Statistics”, TVP, 23:4 (1978), 886; A. A. Novikov, A. S. Holevo, “The Twelfth All-Union Seminar on Probability Theory and Mathematical Statistics”, Theory Probab. Appl., 23:4 (1979), 853
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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