Noncommutative probability, quantum information and statistical decision theory, mathematical statistics of random processes.
Mathematical theory of quantum communication channels was developed, coding theorems of quantum information theory were established, noncommutative statistical decision theory was constructed, the structure of quantum Markov processes was investigated.
Biography
Graduated from the Moscow Institute of Physics and Technology in 1966, dyploma in «Applied mathematics and computer science». From 1969 works in the Steklov Mathematical Institute, Moscow. Candidate of phys-math sciences — 1969, Doctor of of phys-math sciences — 1975, Professor — 1986. List of publications contains nearly 190 titles including five monographs, four of them translated into English and published by the leading foreign Publishing houses (AMS, North Holland, Springer-Verlag). Awards: A. A. Markov Prize, Russian Academy of Sciences for the series of works on the noncommutative probability theory — 1997; Awards of the Russian Academy of Sciences for the best research achievements in 1992, 1995, 2008, 2015; International «Quantum Communication Award» — 1996; A. von Humboldt Research Award — 1999;
Claude E. Shannon Award 2016. Invited speaker at the International Congresses of Mathematicians — Berkeley (1986), Madrid (2006), and many other international and national conferences. Member of the Editorial boards of the journals: «Theory of probability and its applications», «Russian mathematical surveys (Uspekhi)», «Sbornik:mathematics», «Theoretical and mathematical physics», «Izvestiya vuzov: Mathematics», «IEEE Transactions on Information Theory», «Quantum Information Processing», «Reports on Mathematical Physics».
Main publications:
A. S. Holevo, Studies in general theory of statistical decisions, Proc. Steklov Math. Inst., 124, 1978
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, North Holland, 1982
A. S. Holevo, Statistical structure of quantum theory, Lect. Notes Phys., 67, Springer, 2001
A. S. Holevo, Quantum systems, channels, information, DeGruyter, 2012
M. E. Shirokov, A. S. Holevo, Izv. RAN. Ser. Mat., 81:5 (2017) (to appear)
2016
2.
A. S. Holevo, “On the constrained classical capacity of infinite-dimensional covariant quantum channels”, J. Math. Phys., 57:1 (2016), 015203 , 11 pp.
3.
A. S. Holevo, “On the proof of the majorization theorem for quantum Gaussian channels”, Russian Math. Surveys, 71:3 (2016), 585–587
4.
A. S. Holevo, “On a characterization of Gaussian transition operators”, Teor. Veroyatnost. i Primenen., 61:4 (2016), 830–837
5.
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
2015
6.
V. Giovannetti, A. S. Holevo, R. García-Patrón, “A solution of Gaussian optimizer conjecture for quantum channels”, Comm. Math. Phys., 334:3 (2015), 1553–1571 (cited: 8) (cited: 4) (cited: 13) (cited: 8)
7.
V. Giovannetti, A. S. Holevo, A. Mari, “Majorization and additivity for multimode bosonic Gaussian channels”, Theoret. and Math. Phys., 182:2 (2015), 284–293 (cited: 7) (cited: 5) (cited: 5) (cited: 6)
8.
A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367 (cited: 9) (cited: 1) (cited: 1) (cited: 4)
9.
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
10.
G. De Palma, A. Mari, V. Giovannetti, A. S. Holevo, “Normal form decomposition for Gaussian-to-Gaussian superoperators”, J. Math. Phys., 56:5 (2015), 052202 , 19 pp. (cited: 3) (cited: 3) (cited: 3)
11.
A. S. Kholevo, M. E. Shirokov, “Kriterii slaboi kompaktnosti dlya semeistv obobschennykh kvantovykh ansamblei i ego sledstviya”, TVP, 60:2 (2015), 402–408; 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
12.
Y. I. Bogdanov, B. I. Bantysh, V. F. Lukichev, A. A. Orlikovsky, A. S. Holevo, “Entanglement dynamics in quantum operations using superconducting phase qubits”, Bulletin of the Russian Academy of Sciences: Physics, 78:1 (2014), 1–5 (cited: 1) (cited: 1) (cited: 1)
13.
A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14 (cited: 1)
14.
A. A. Kuznetsova, A. S. Kholevo, “Teoremy kodirovaniya dlya gibridnykh kanalov. II”, TVP, 59:1 (2014), 168–178; A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels. II”, Theory Probab. Appl., 59:1 (2015), 145–154
15.
A. Mari, V. Giovannetti, A. S. Holevo, “Quantum state majorization at the output of bosonic Gaussian channels”, Nature Communications, 5 (2014), 3826 , 5 pp. (cited: 26) (cited: 26)
16.
V. Giovannetti, R. Garcia-Patron, N. J. Cerf, A. S. Holevo, “Ultimate classical communication rates of quantum optical channels”, Nature Photonics, 8:10 (2014), 216 , 6 pp. (cited: 35) (cited: 23)
17.
A. S. Kholevo, “Quantum Gaussian optimizer problem”, New Horizons in Statistical Decision Theory (Oberwolfach, 7–13 September 2014), Oberwolfach Reports, 41/2014, Mathematisches Forschungsinstitut Oberwolfach, 2014, 28–31
2013
18.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction, De Gruyter, Berlin–Boston, 2013 , 370 pp. (rasshirennoe i ispravlennoe izdanie angliiskogo perevoda monografii) (cited: 31)
19.
A. S. Holevo, “Information capacities of quantum measurement channels”, 19e Tsentralno-evropeiskoe soveschanie po kvantovoi optike (Sinaia, Romania, 2–6.07.2012), Phys. Scr., T153, 2013, 014034 , 4 pp. (cited: 6) (cited: 5) (cited: 5)
20.
A. S. Holevo, “Extreme bosonic linear channels”, Theoret. and Math. Phys., 174:2 (2013), 288–297 (cited: 6) (cited: 5) (cited: 5) (cited: 4)
21.
A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31 (cited: 4) (cited: 4) (cited: 3)
22.
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
23.
A. A. Kuznetsova, A. S. Kholevo, “Teoremy kodirovaniya dlya gibridnykh kanalov”, TVP, 58:2 (2013), 298–324 (cited: 1) ; A. A. Kuznetsova, A. S. Holevo, “Coding Theorems for Hybrid Channels”, Theory Probab. Appl., 58:2 (2014), 264–285 (cited: 1) (cited: 1) (cited: 1)
24.
V. Giovannetti, A. S. Holevo, R. Garcia-Patron, A solution of the Gaussian optimizer conjecture, 2013 , Newton Institute preprint NI13068-MQI, arXiv: 1312.2251
2012
25.
A. S. Holevo, V. Giovannetti, “Quantum channels and their entropic characteristics”, Rep. Prog. Phys., 75 (2012), 046001 , 45 pp. (cited: 5) (cited: 51) (cited: 35) (cited: 34)
26.
A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10 (cited: 17) (cited: 18) (cited: 19)
2011
27.
A. S. Holevo, “Entropy gain and the Choi–Jamiolkowski correspondence for infinite-dimensional quantum evolutions”, Theoret. and Math. Phys., 166:1 (2011), 123–138 (cited: 12) (cited: 11) (cited: 11) (cited: 13)
28.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, 2nd edition, Edizioni della Normale, Pisa, 2011 (cited: 19)
29.
F. Caruso, J. Eisert, V. Giovannetti, A. S. Holevo, “The optimal unitary dilation for bosonic Gaussian channels”, Phys. Rev. A, 84 (2011), 022306 , 10 pp. (cited: 12) (cited: 10) (cited: 14)
30.
A. S. Holevo, “The Choi-Jamiolkowski forms of quantum Gaussian channels”, J. Math. Phys., 52 (2011), 042202 , 12 pp. (cited: 4) (cited: 11) (cited: 8) (cited: 10)
31.
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
32.
A. S. Holevo, “The entropy gain of quantum channels”, IEEE International Symposium on Information Theory (ISIT) (Jule 31 – August 05, 2011, St. Petersburg, Russia), 2011, 289–292 (cited: 1)
33.
A. S. Holevo, “Statistical inference for quantum systems”, International Encyclopedia of Statistical Science, eds. M. Lovric, Springer, 2011, 1420–1423
2010
34.
A. S. Kholevo, Kvantovye sistemy, kanaly, informatsiya, MTsNMO, M., 2010 , 328 pp.
35.
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
36.
A. S. Holevo, “The entropy gain of infinite-dimensional quantum evolutions”, Dokl. Math., 82:2 (2010), 730–731 (cited: 5) (cited: 5) (cited: 5) (cited: 6)
37.
A. S. Kholevo, “Kvantovaya teoriya informatsii. Kanaly i propusknye sposobnosti”, Informatsionnye tekhnologii i vychislitelnye sistemy, 3 (2010), 39–46
38.
A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218 (cited: 8) (cited: 8) (cited: 9)
39.
V. Giovannetti, A. S. Holevo, S. Lloyd, L. Maccone, “Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results”, J. Phys. A, 43:41 (2010), 415305 , 10 pp. (cited: 2) (cited: 12) (cited: 16) (cited: 15)
40.
T. Heinosaari, A. S. Holevo, M. M. Wolf, “The semigroup structure of Gaussian channels”, Quantum Inf. Comput., 10:7-8 (2010), 619–635 (cited: 2) (cited: 17) (cited: 6) (cited: 5)
2009
41.
A. S. Holevo, J.-P. Pellonpää, “Extreme Covariant Observables for Type I Symmetry Groups”, Found. Phys., 39:6 (2009), 625–641 (cited: 1) (cited: 3) (cited: 3) (cited: 3)
42.
A. S. Kholevo, “Kvantovaya teoriya informatsii”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 451–453
43.
A. S. Kholevo, K. A. Valiev, “Kvantovyi kompyuter”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 472–473
2008
44.
F. Caruso, J. Eisert, V. Giovannetti, A. S. Holevo, “Multi-mode bosonic Gaussian channels”, New J. Phys., 10 (2008), 083030 , 33 pp. (cited: 35) (cited: 37)
45.
A. S. Holevo, V. Giovannetti, “Quantum shared broadcasting”, Quantum Inf. Process., 7:2-3 (2008), 55–69 (cited: 1) (cited: 5) (cited: 5) (cited: 5)
46.
A. S. Holevo, “Entanglement-Breaking Channels in Infinite Dimensions”, Problems Inform. Transmission, 44:3 (2008), 171–184 (cited: 36) (cited: 38) (cited: 38) (cited: 39)
47.
M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90 (cited: 10) (cited: 8) (cited: 8) (cited: 10)
48.
A. S. Kholevo, “Kvantovaya informatika: proshloe, nastoyaschee, buduschee”, V mire nauki, 2008, no. 7, 68–75http://www.sciam.ru/2008/7/inform.shtml (cited: 1)
2007
49.
A. S. Holevo, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11 (cited: 43) (cited: 42) (cited: 42) (cited: 45)
2006
50.
A. S. Holevo, “The additivity problem in quantum information theory”, International Congress of Mathematicians, Vol. III, Eur. Math. Soc., Zürich, 2006, 999–1018 (cited: 10)
51.
N. Datta, M. Fukuda, A. S. Holevo, “Complementarity and additivity for covariant channels”, Quantum Inf. Process., 5:3 (2006), 179–207 (cited: 5) (cited: 11) (cited: 10) (cited: 13)
52.
F. Caruso, V. Giovannetti, A. S. Holevo, “One-mode Bosonic Gaussian channels: a full weak-degradability classification”, New Journal of Physics, 8 (2006), 310 (cited: 48) (cited: 49)
53.
A. S. Holevo, “Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory”, Russian Math. Surveys, 61:2 (2006), 301–339 (cited: 4) (cited: 3) (cited: 3) (cited: 4)
54.
A. S. Kholevo, “Komplementarnye kanaly i problema additivnosti”, TVP, 51:1 (2006), 133–143 (cited: 35) (cited: 27) (cited: 13); A. S. Holevo, “Complementary channels and the additivity problem”, Theory Probab. Appl., 51:1 (2007), 92–100 (cited: 22) (cited: 13) (cited: 11)
55.
A. S. Holevo, “Locating a photon:position observables and an uncertainty relation”, Russian Microelectronics, 35:1 (2006), 21–30
56.
N. Datta, A. S. Holevo, Yu. M. Suhov, “Additivity for transpose depolarizing channels”, Int. J. Quant. Inform.,, 4:1 (2006), 85–98 (cited: 4) (cited: 4) (cited: 4)
57.
A. S. Holevo, “Quantum channels: classical capacity”, Encyclopedia of Mathematical Physics, Academic Press, 2006, 142–144
2005
58.
R. F. Werner, A. S. Holevo, M. E. Shirokov, “On the notion of entanglement in Hilbert spaces”, Russian Math. Surveys, 60:2 (2005), 359–360 (cited: 10) (cited: 18)
59.
N. Datta, A. S. Holevo, Yu. M. Sukhov, “On a Sufficient Additivity Condition in Quantum Information Theory”, Problems Inform. Transmission, 41:2 (2005), 76–90 (cited: 3) (cited: 3) (cited: 4)
60.
A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98 (cited: 22) (cited: 22) (cited: 22) (cited: 18)
61.
A. S. Holevo, “The additivity problem and constrained quantum channels”, Proc. Int. Soc. Opt. Eng., 5833 (2005), 196-201
62.
A. S. Holevo, “Additivity conjecture and covariant channels”, Int. J. Quant., 3:1 (2005), 41-48 (cited: 12) (cited: 12) (cited: 13)
2004
63.
A. S. Holevo, M. E. Shirokov, “On Shor's channel extension and constrained channels”, Comm. Math. Phys., 249:2 (2004), 417–430 (cited: 6) (cited: 23) (cited: 29) (cited: 25)
64.
A. S. Holevo, M. E. Shirokov, “The additivity problem for constrained quantum channels”, Russian Math. Surveys, 59:2 (2004), 385–387
65.
A. S. Kholevo, “Asimptoticheskoe otsenivanie parametra sdviga kvantovogo sostoyaniya”, TVP, 49:2 (2004), 335–350 (cited: 4) ; A. S. Holevo, “Asymptotic estimation of a shift parameter of a quantum state”, Theory Probab. Appl., 49:2 (2005), 207–220 (cited: 3) (cited: 4) (cited: 4)
2003
66.
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
67.
A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, 2-e izd., Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003 , 410 pp.
68.
A. S. Kholevo, Statisticheskaya struktura kvantovoi teorii, Institut kompyuternykh issledovanii, Izhevsk, 2003
69.
A. S. Kholevo, “Klassicheskie propusknye sposobnosti kvantovogo kanala s ogranicheniem na vkhode”, TVP, 48:2 (2003), 359–374 (cited: 19) (cited: 9) ; A. S. Holevo, “Entanglement-assisted capacities of constrained quantum channels”, Theory Probab. Appl., 48:2 (2004), 243–255 (cited: 3) (cited: 13) (cited: 13)
70.
A. S. Holevo, “Optimal receiver of a binary coherent signals based on the principle of optical feedback”, Laser Physics, 13:12 (2003), 1558–1561 (cited: 11) (cited: 2) (cited: 2)
71.
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, “K 80-letiyu B. A. Sevastyanova”, TVP, 48:4 (2003), 785 (cited: 1) (cited: 1); 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
72.
A. S. Holevo, “On states, channels, and purification”, Quantum Inf. Process., 1:1-2 (2002), 1–4 (cited: 1) (cited: 1)
73.
R. F. Werner, A. S. Holevo, “Counterexample to an additivity conjecture for output purity of quantum channels”, Quantum information theory, J. Math. Phys., 43, no. 9, 2002, 4353–4357 (cited: 38) (cited: 77) (cited: 82) (cited: 84)
74.
A. S. Holevo, “On entanglement-assisted classical capacity”, Quantum information theory, J. Math. Phys., 43, no. 9, 2002, 4326–4333 (cited: 14) (cited: 42) (cited: 45)
75.
A. S. Kholevo, Vvedenie v kvantovuyu teoriyu informatsii, MTsNMO, M., 2002 , 128 pp.
76.
G. G. Amosov, A. S. Kholevo, “O gipoteze multiplikativnosti dlya kvantovykh kanalov svyazi”, TVP, 47:1 (2002), 143–146 (cited: 17) (cited: 8) ; G. G. Amosov, A. S. Holevo, “On the multiplicativity hypothesis for quantum communication channels”, Theory Probab. Appl., 47:1 (2003), 123–127 (cited: 7) (cited: 6) (cited: 5)
77.
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
78.
A. S. Holevo, Statistical structure of quantum theory, Lecture Notes in Physics. Monographs, 67, Springer-Verlag, Berlin, 2001 , x+159 pp. (cited: 67)
79.
A. S. Holevo, “Coding theorems of quantum information theory”, XIIIth International Congress on Mathematical Physics (London, 2000), Int. Press, Boston, MA, 2001, 415–422
80.
A. S. Holevo, “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory”, Math. Methods Statist., 10:1 (2001), 6–22
81.
A. S. Holevo, “An invitation to quantum estimation”, Math. Methods Statist., 10:1 (2001), 1–5
82.
A. S. Holevo, “Lévy processes and continuous quantum measurements”, Lévy processes, Birkhäuser Boston, Boston, MA, 2001, 225–239 (cited: 1)
83.
A. S. Holevo, R. F. Werner, “Evaluating capacities of Bosonic Gaussian channels”, Phys. Rev. A, 63 (2001), 032312 , 13 pp. (cited: 221) (cited: 79)
2000
84.
A. S. Holevo, M. Sohma, O. Hirota, “Error exponents for quantum channels with constrained inputs”, Rep. Math. Phys., 46:3 (2000), 343–358 (cited: 2) (cited: 8) (cited: 9) (cited: 9)
85.
A. S. Holevo, “Reliability function of general classical-quantum channel”, IEEE Trans. Inform. Theory, 46:6 (2000), 2256–2261 (cited: 10) (cited: 18) (cited: 17) (cited: 18)
86.
G. G. Amosov, A. S. Holevo, R. F. Werner, “On the Additivity Conjecture in Quantum Information Theory”, Problems Inform. Transmission, 36:4 (2000), 305–313
1999
87.
A. S. Holevo, M. Sohma, O. Hirota, “The capacity of quantum Gaussian channels”, Phys. Rev. A, 59:3 (1999), 1820–1828 (cited: 136) (cited: 135) (cited: 134)
88.
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
89.
M. V. Burnashev, A. S. Holevo, “Letter to the Editor”, Problems Inform. Transmission, 35:1 (1999), 93–94
1998
90.
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
91.
A. S. Holevo, “Covariant quantum dynamical semigroups: unbounded generators”, Irreversibility and causality (Goslar, 1996), Lecture Notes in Phys., 504, Springer, Berlin, 1998, 67–81 (cited: 8)
92.
A. S. Holevo, “Radon-Nikodým derivatives of quantum instruments”, J. Math. Phys., 39:3 (1998), 1373–1387 (cited: 10) (cited: 22) (cited: 21) (cited: 22)
93.
A. S. Holevo, “The capacity of the quantum channel with general signal states”, IEEE Trans. Inform. Theory, 44:1 (1998), 269–273 (cited: 108) (cited: 544) (cited: 539) (cited: 567)
94.
A. S. Holevo, “Quantum coding theorems”, Russian Math. Surveys, 53:6 (1998), 1295–1331 (cited: 84) (cited: 66) (cited: 85)
95.
M. V. Burnashev, A. S. Holevo, “On the Reliability Function for a Quantum Communication Channel”, Problems Inform. Transmission, 34:2 (1998), 97–107
96.
A. S. Kholevo, “Mezhdunarodnyi simpozium po teorii informatsii 1998 g.”, TVP, 43:4 (1998), 823–824; A. S. Holevo, “International symposium on information theory 1998”, Theory Probab. Appl., 43:4 (1999), 685–686
1997
97.
M. V. Burnashev, A. S. Holevo, On reliability function of quantum communication channel, 1997 , 8 pp., arXiv: quant-ph/9703013
98.
A. S. Holevo, “On covariant instruments in quantum measurement theory”, Quantum Communication, Computing and Measurement. Proc. of the Third International Conference (Shizuoka, 25-30.09.1996.), eds. O. Hirota, A. S. Holevo and C. Caves, Plenum Press, New York - London, 1997, 223–232
1996
99.
A. S. Holevo, “The structure of classical noise”, Analysis, geometry and probability, Texts Read. Math., 10, Hindustan Book Agency, Delhi, 1996, 73–86
100.
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 (cited: 4)
101.
A. S. Holevo, “Exponential formulae in quantum stochastic calculus”, Proc. Roy. Soc. Edinburgh Sect. A, 126:2 (1996), 375–389 (cited: 3) (cited: 5) (cited: 5)
102.
A. S. Holevo, “On dissipative stochastic equations in a Hilbert space”, Probab. Theory Related Fields, 104:4 (1996), 483–500 (cited: 14) (cited: 31) (cited: 29) (cited: 29)
103.
A. S. Holevo, “Covariant quantum Markovian evolutions”, J. Math. Phys., 37:4 (1996), 1812–1832 (cited: 7) (cited: 31) (cited: 32)
104.
A. S. Holevo, M. Sasaki, T. S. Usuda, O. Hirota, “Application of the Jaynes-Kummings model for the detection of nonorthogonal quantum states”, Phys. Rev. A, 53 (1996), 1273–1279 (cited: 16)
105.
A. S. Holevo, “There exists a non-standard dynamical semigroup on $\mathfrak L(\mathscr H)$”, Russian Math. Surveys, 51:6 (1996), 1206–1207 (cited: 1)
106.
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 (cited: 1); B. M. Gurevich, I. A. Ibragimov, R. A. Minlos, I. A. Ovseevich, V. I. Oseledets, M. S. Pinsker, V. V. Prelov, Yu. V. Prokhorov, Ya. G. Sinai, A. S. Holevo, A. N. Shiryaev, “Roland L'vovich Dobrushin (20 July 1919 – 12 November 1995)”, Theory Probab. Appl., 41:1 (1997), 132–136
1995
107.
A. Barchielli, A. S. Holevo, “Constructing quantum measurement processes via classical stochastic calculus”, Stochastic Process. Appl., 58:2 (1995), 293–317 (cited: 17) (cited: 41) (cited: 19) (cited: 41)
108.
A. S. Holevo, “On the structure of covariant dynamical semigroups”, J. Funct. Anal., 131:2 (1995), 255–278 (cited: 3) (cited: 19) (cited: 15)
109.
A. S. Holevo, “On translation-covariant quantum Markov equations”, Izv. Math., 59:2 (1995), 427–443 (cited: 12)
110.
A. S. Holevo, “Excessive maps, “arrival times” and perturbation of dynamical semigroups”, Izv. Math., 59:6 (1995), 1311–1325
1993
111.
A. S. Holevo, “A note on covariant dynamical semigroups”, Rep. Math. Phys., 32:2 (1993), 211–216 (cited: 9) (cited: 10) (cited: 32)
112.
A. S. Holevo, “On conservativity of covariant dynamical semigroups” (Toruń, 1992), Rep. Math. Phys., Proceedings of the XXV Symposium on Mathematical Physics, 33, no. 1-2, 1993, 95–110 (cited: 5) (cited: 7) (cited: 20)
113.
A. S. Kholevo, “Structure of covariant dynamical semigroups”, Russian Acad. Sci. Dokl. Math., 47:1 (1993), 161–167
114.
A. Barchielli, A. S. Holevo, G. Lupieri, “An analogue of Hunt's representation theorem in quantum probability”, J. Theoret. Probab., 6:2 (1993), 231–265 (cited: 1) (cited: 1) (cited: 7)
115.
A. S. Kholevo, “On the Lévy–Khinchin formula in noncommutative probability theory”, Theory Probab. Appl., 38:4 (1993), 660–672
116.
N. S. Bakhvalov, A. A. Borovkov, R. L. Dobrushin, A. V. Zabrodin, V. M. Zolotarev, I. A. Ibragimov, Yu. V. Prokhorov, B. A. Sevast'yanov, Ya. G. Sinai, A. V. Skorokhod, V. A. Statulyavichus, R. Z. Khas'minskii, A. S. Kholevo, D. M. Chibisov, A. N. Shiryaev, “Memorial: Nikolai Nikolaevitch Chentsov”, Theory Probab. Appl., 38:3 (1993), 506–515 (cited: 1)
117.
V. I. Arnol'd, N. S. Bakhvalov, K. V. Brushlinskii, I. M. Gel'fand, R. L. Dobrushin, A. V. Zabrodin, I. A. Ibragimov, S. P. Kurdyumov, S. P. Novikov, D. E. Okhotsimskii, Yu. V. Prokhorov, Yu. B. Radvogin, Ya. G. Sinai, R. Z. Khas'minskii, A. S. Holevo, A. N. Shiryaev, T. M. Eneev, “Nikolai Nikolaevich Chentsov (obituary)”, Russian Math. Surveys, 48:2 (1993), 161–166
1992
118.
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 (cited: 7)
1991
119.
A. S. Holevo, “Statistical inference for quantum processes”, Quantum aspects of optical communications (Paris, 1990), Lecture Notes in Phys., 378, Springer, Berlin, 1991, 127–137 (cited: 18)
120.
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 (cited: 1)
121.
A. S. Holevo, “Quantum probability and quantum statistics”, Probability theory – 8, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 83, VINITI, Moscow, 1991, 5–132
1990
122.
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
123.
A. S. Holevo, “An analog of the Itô decomposition for multiplicative processes with values in a Lie group”, Quantum probability and applications, V (Heidelberg, 1988), Lecture Notes in Math., 1442, Springer, Berlin, 1990, 211–215 (cited: 2) (cited: 5)
1989
124.
A. S. Holevo, “Limit theorems for repeated measurements and continuous measurement processes”, Quantum probability and applications, IV (Rome, 1987), Lecture Notes in Math., 1396, Springer, Berlin, 1989, 229–255 (cited: 12)
125.
A. S. Kholevo, “Uslovno polozhitelno opredelennye funktsii v kvantovoi teorii veroyatnostei”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Nov. dostizh., 36, VINITI, M., 1989, 103–147 (cited: 1) ; A. S. Holevo, “Conditionally positive-definite functions in quantum probability theory”, J. Soviet Math., 56:5 (1991), 2670–2697
126.
A. S. Kholevo, “Kvantovoe stokhasticheskoe ischislenie”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Nov. dostizh., 36, VINITI, M., 1989, 3–28 (cited: 3) (cited: 4) ; A. S. Holevo, “A quantum stochastic calculus”, J. Soviet Math., 56:5 (1991), 2609–2624 (cited: 15)
127.
A. S. Kholevo, “Stokhasticheskie predstavleniya kvantovykh dinamicheskikh polugrupp”, 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 (cited: 1) (cited: 2) ; A. S. Holevo, “Stochastic representations of quantum dynamical semi-groups”, Proc. Steklov Inst. Math., 191 (1992), 145–154
1988
128.
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. (cited: 1)
129.
A. S. Holevo, “A noncommutative generalization of conditionally positive definite functions”, Quantum probability and applications, III (Oberwolfach, 1987), Lecture Notes in Math., 1303, Springer, Berlin, 1988, 128–148 (cited: 1) (cited: 15)
1987
130.
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
131.
A. S. Holevo, “Lévy–Khintchine Representation in Quantum Theory of Probability”, Theory Probab. Appl., 32:1 (1987), 131–136 (cited: 1)
132.
A. S. Holevo, “Quantum estimation”, Adv. Statist. Signal Proc., v. 1, JAI Press Inc., 1987, 157–202
1986
133.
A. S. Kholevo, “Ob odnom obobschenii kanonicheskogo kvantovaniya”, Izv. AN SSSR. Ser. matem., 50:1 (1986), 181–194 (cited: 7) (cited: 1) ; A. S. Kholevo, “On a generalization of canonical quantization”, Math. USSR-Izv., 28:1 (1987), 175–188
134.
A. S. Kholevo, “Bezgranichno delimye izmereniya v kvantovoi teorii veroyatnostei”, TVP, 31:3 (1986), 560–564 (cited: 1) ; A. S. Holevo, “Infinite-divisible instruments in quantum probability theory”, Theory Probab. Appl., 31:3 (1987), 493–497 (cited: 1)
1985
135.
A. S. Holevo, “Statistical definition of observable and the structure of statistical models”, Rep. Math. Phys., 22:3 (1985), 385–407 (cited: 3) (cited: 12)
136.
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.
137.
A. S. Holevo, “On the principle of quantum nondemolition measurements”, Theoret. and Math. Phys., 65:3 (1985), 1250–1255 (cited: 4)
1984
138.
A. S. Holevo, “Covariant measurements and imprimitivity systems”, Quantum probability and applications to the quantum theory of irreversible processes (Villa Mondragone, 1982), Lecture Notes in Math., 1055, Springer, Berlin, 1984, 153–172 (cited: 2) (cited: 27)
1983
139.
A. S. Holevo, “Bounds for generalized uncertainty of the shift parameter”, Probability theory and mathematical statistics (Tbilisi, 1982), Lecture Notes in Math., 1021, Springer, Berlin, 1983, 243–251 (cited: 5)
140.
N. A. Bogomolov, A. S. Kholevo, “A characterization of the covariant resolutions of the identity”, Funct. Anal. Appl., 17:2 (1983), 131–132
141.
A. S. Holevo, “Generalized imprimitivity systems for abelian groups”, Soviet Math. (Iz. VUZ), 27:2 (1983), 53–80
142.
A. S. Holevo, “On measurements of the parameters of a quantum random process”, Theoret. and Math. Phys., 57:3 (1983), 1238–1247
1982
143.
A. S. Holevo, “Testing statistical hypotheses in quantum theory”, Probab. Math. Statist., 3:1 (1982), 113–126 (1983) (cited: 1)
144.
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. (cited: 139)
145.
A. S. Holevo, “Quantum-probabilistic investigation of the statistics of readings, using a “Dolinar device””, Soviet Math. (Iz. VUZ), 26:8 (1982), 1–20
1981
146.
H. A. Bogomolov, A. S. Kholevo, “Razlozheniya edinitsy, kovariantnye otnositelno predstavleniya abelevoi lokalno kompaktnoi gruppy”, Tr. NIVTs MGU, M., 1981, 45–59
1980
147.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Nauka, Moscow, 1980 , 320 pp.
1979
148.
A. S. Holevo, “Covariant measurements and uncertainty relations”, Rep. Math. Phys., 16:3 (1979), 385–400 (cited: 15) (cited: 16) (cited: 54)
149.
A. S. Holevo, “On Capacity of a Quantum Communications Channel”, Problems Inform. Transmission, 15:4 (1979), 247–253 (cited: 58)
1978
150.
A. S. Holevo, “Estimation of shift parameters of a quantum state”, Rep. Math. Phys., 13:3 (1978), 379–399 (cited: 3) (cited: 38)
151.
N. P. Rasulov, A. S. Kholevo, “Odna zadacha regressii dlya protsessov s nepreryvnym vremenem”, TVP, 23:4 (1978), 762–771 (cited: 1) (cited: 2) ; N. P. Rasulov, A. S. Holevo, “A regression problem for continuous time series”, Theory Probab. Appl., 22:4 (1979), 731–740 (cited: 1)
152.
A. S. Kholevo, “Ob asimptoticheski optimalnom razlichenii gipotez v kvantovoi statistike”, TVP, 23:2 (1978), 429–432 (cited: 5) (cited: 13) ; A. S. Holevo, “On asymptotically optimal hypotheses testing in quantum statistics”, Theory Probab. Appl., 23:2 (1979), 411–415 (cited: 11)
153.
A. A. Novikov, A. S. Kholevo, “Dvenadtsataya Vsesoyuznaya shkola-kollokvium po teorii veroyatnostei i matematicheskoi statistike”, 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
1977
154.
A. S. Holevo, “Commutation superoperator of a state and its applications to the noncommutative statistics”, Rep. Mathematical Phys., 12:2 (1977), 251–271 (cited: 3)
155.
A. S. Holevo, “Problems in the mathematical theory of quantum communication channels”, Rep. Mathematical Phys., 12:2 (1977), 273–278 (cited: 9) (cited: 20) (cited: 47)
1976
156.
A. S. Kholevo, “Issledovaniya po obschei teorii statisticheskikh reshenii”, Tr. MIAN SSSR, 124, 1976, 3–140 , 141 pp. (cited: 6) (cited: 6) (cited: 6) ; A. S. Kholevo, “Investigations in the general theory of statistical decisions”, Proc. Steklov Inst. Math., 124 (1978), 1–140
157.
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
158.
A. S. Kholevo, “Optimalnoe izmerenie amplitud kompleksnykh signalov na fone kvantovogo shuma”, Trudy 4-go Mezhdunarodnogo simpoziuma po teorii informatsii, Leningrad, 1976
159.
A. S. Kholevo, “Integral po mere so znacheniyami v prostranstve, sopryazhennom k chastichno uporyadochennomu banakhovu prostranstvu”, 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
1975
160.
A. S. Holevo, “On a vector-valued integral in the “noncommutative” statistical decision theory”, J. Multivariate Anal., 5:4 (1975), 462–465
161.
A. S. Holevo, “Some statistical problems for quantum Gaussian states”, IEEE Trans. Information Theory, IT-21:5 (1975), 533–543 (cited: 1) (cited: 29) (cited: 27)
162.
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
1974
163.
A. S. Kholevo, “The theory of statistical decisions on an operator algebra”, Sov. Math. Dokl., 15 (1974), 1276–1281 (1975)
164.
A. S. Kholevo, “Optimal measurement of the mean value of a Gaussian state”, Engrg. Cybernetics, 12:5 (1974), 128–130
165.
A. S. Holevo, “Remarks on Optimal Quantum Measurements”, Problems Inform. Transmission, 10:4 (1974), 317–320
1973
166.
A. S. Holevo, “On the general problem of mean estimation”, J. Multivariate Anal., 3 (1973), 262–275 (cited: 1)
167.
A. S. Holevo, “Statistical decision theory for quantum systems”, J. Multivariate Anal., 3 (1973), 337–394 (cited: 39) (cited: 48) (cited: 255)
168.
A. S. Holevo, “A Generalization of the Rao–Cramér Inequality”, Theory Probab. Appl., 18:2 (1973), 359–362
169.
A. S. Holevo, “Information-Theoretical Aspects of Quantum Measurement”, Problems Inform. Transmission, 9:2 (1973), 110–118
170.
A. S. Holevo, “Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel”, Problems Inform. Transmission, 9:3 (1973), 177–183
171.
A. S. Holevo, “Optimal quantum measurements”, Theoret. and Math. Phys., 17:3 (1973), 1172–1177 (cited: 3)
172.
A. S. Holevo, “On the quasiequivalence of quasifree states on the $C^*$-algebra of CAR”, Theoret. and Math. Phys., 14:2 (1973), 107–111
173.
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 (cited: 6)
1972
174.
A. S. Holevo, “An analogue of statistical decision theory and noncommutative probability theory”, Trudy Moskov. Mat. Obšč., 26, 1972, 133–149
175.
A. S. Kholevo, “Ob otsenivanii funktsii ot srednego znacheniya”, TVP, 17:3 (1972), 573–577; A. S. Kholevo, “On estimating functions of the mean”, Theory Probab. Appl., 17:3 (1973), 543–547
176.
A. S. Kholevo, “Nekotorye statisticheskie zadachi dlya kvantovykh polei”, TVP, 17:2 (1972), 360–365; A. S. Kholevo, “Some statistical problems for quantum fields”, Theory Probab. Appl., 17:2 (1973), 347–351
177.
A. S. Holevo, “On the Mathematical Theory of Quantum Communication Channels”, Problems Inform. Transmission, 8:1 (1972), 47–54
178.
A. S. Holevo, “On quasiequivalence of locally normal states”, Theoret. and Math. Phys., 13:2 (1972), 1071–1082 (cited: 4)
1971
179.
A. S. Holevo, “Quasifree states of the $C^*$ algebra of CCR. II”, Theoret. and Math. Phys., 6:2 (1971), 103–107 (cited: 2)
180.
A. S. Holevo, “Quasi-free states on the $C^*$ algebra of CCR”, Theoret. and Math. Phys., 6:1 (1971), 1–12 (cited: 2)
181.
A. S. Holevo, “On asymptotic normality of estimates of regression coefficients”, Theory Probab. Appl., 16:4 (1971), 707–711
182.
A. S. Holevo, “On asymptotic efficiency of pseudo-best estimators”, Theory Probab. Appl., 16:3 (1971), 516–527
183.
A. S. Holevo, “Almost periodic signal estimations”, Theory Probab. Appl., 16:2 (1971), 249–263
1970
184.
A. S. Holevo, “Quantum Characteristic Functions”, Problems Inform. Transmission, 6:4 (1970), 316–321
1969
185.
A. S. Holevo, “On estimates of regression coefficients”, Theory Probab. Appl., 4:1 (1969), 79–104
1967
186.
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
187.
A. S. Kholevo, “On Sequential Estimates of Parameters”, Theory Probab. Appl., 12:1 (1967), 147–152
1965
188.
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
189.
A. S. Holevo, “Automata which predict a random process”, Soviet Physics Dokl., 10 (1965), 816–818
On the 100th anniversary of Claude Shannon 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 Seminar of the Department of Probability Theory "Stochastic Analysis: Theory and Applications", Steklov Mathematical Institute of RAS September 3, 2015 13:00
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
2017
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