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
A. S. Holevo, “Mathematical foundations of quantum informatics”, Lekts. Kursy NOC, 30, 2018, 3–118
2017
3.
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
4.
A. S. Holevo, “ON THE CLASSICAL CAPACITY OF A CHANNEL WITH STATIONARY QUANTUM GAUSSIAN NOISE”, THEORY PROBAB. APPL., 62:4 (2018), 534–551
2017
5.
I. Siemon, A. S. Holevo, R. F. Werner, “Unbounded generators of dynamical semigroups”, Open Syst. Inf. Dyn., 24:4 (2017), 1740015 , 24 pp. (cited: 1) (cited: 1)
6.
A. S. Holevo, “On the quantum Gaussian optimizers conjecture in the case $q=p$”, Russian Math. Surveys, 72:6 (2017), 1177–1179 (cited: 1) (cited: 2)
2016
7.
A. S. Holevo, “On the constrained classical capacity of infinite-dimensional covariant quantum channels”, J. Math. Phys., 57:1 (2016), 15203 , 11 pp. (cited: 1) (cited: 3) (cited: 4)
8.
A. S. Holevo, “On the proof of the majorization theorem for quantum Gaussian channels”, Russian Math. Surveys, 71:3 (2016), 585–587 (cited: 1)
2017
9.
A. S. Holevo, “On a characterization of Gaussian transition operators”, Theory Probab. Appl., 61:4 (2017), 715–718
2016
10.
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 (cited: 10) (cited: 4) (cited: 24) (cited: 8)
13.
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: 10) (cited: 5) (cited: 5) (cited: 11)
14.
A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367 (cited: 19) (cited: 1) (cited: 1) (cited: 12)
15.
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 (cited: 1) (cited: 1)
16.
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: 8) (cited: 12)
2016
17.
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
18.
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)
19.
A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14 (cited: 1)
2015
20.
A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels. II”, Theory Probab. Appl., 59:1 (2015), 145–154
2014
21.
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: 36) (cited: 37)
22.
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: 60) (cited: 23)
23.
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
24.
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: 33)
25.
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: 6)
26.
A. S. Holevo, “Extreme bosonic linear channels”, Theoret. and Math. Phys., 174:2 (2013), 288–297 (cited: 8) (cited: 5) (cited: 5) (cited: 6)
27.
A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31 (cited: 7) (cited: 4) (cited: 6)
28.
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
29.
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) (cited: 1)
2013
30.
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
31.
A. S. Holevo, V. Giovannetti, “Quantum channels and their entropic characteristics”, Rep. Prog. Phys., 75 (2012), 046001 , 45 pp. (cited: 6) (cited: 60) (cited: 35) (cited: 66)
32.
A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10 (cited: 21) (cited: 18) (cited: 23)
2011
33.
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: 19) (cited: 11) (cited: 11) (cited: 19)
34.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, 2nd edition, Edizioni della Normale, Pisa, 2011 (cited: 19)
35.
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: 13) (cited: 10) (cited: 15)
36.
A. S. Holevo, “The Choi-Jamiolkowski forms of quantum Gaussian channels”, J. Math. Phys., 52 (2011), 042202 , 12 pp. (cited: 4) (cited: 16) (cited: 8) (cited: 18)
37.
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
38.
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: 2)
39.
A. S. Holevo, “Statistical inference for quantum systems”, International Encyclopedia of Statistical Science, eds. M. Lovric, Springer, 2011, 1420–1423
2010
40.
A. S. Kholevo, Kvantovye sistemy, kanaly, informatsiya, MTsNMO, M., 2010 , 328 pp. https://www.mccme.ru/free-books/holevo-quantum.pdf
41.
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
42.
A. S. Holevo, “The entropy gain of infinite-dimensional quantum evolutions”, Dokl. Math., 82:2 (2010), 730–731 (cited: 11) (cited: 5) (cited: 5) (cited: 12)
43.
A. S. Kholevo, “Kvantovaya teoriya informatsii. Kanaly i propusknye sposobnosti”, Informatsionnye tekhnologii i vychislitelnye sistemy, 3 (2010), 39–46
44.
A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218 (cited: 10) (cited: 8) (cited: 11)
45.
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: 14) (cited: 16) (cited: 22)
46.
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: 22) (cited: 6) (cited: 8)
2009
47.
A. S. Holevo, J.-P. Pellonpää, “Extreme Covariant Observables for Type I Symmetry Groups”, Found. Phys., 39:6 (2009), 625–641 (cited: 1) (cited: 4) (cited: 3) (cited: 4)
48.
A. S. Kholevo, “Kvantovaya teoriya informatsii”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 451–453
49.
A. S. Kholevo, K. A. Valiev, “Kvantovyi kompyuter”, Bolshaya Rossiiskaya entsiklopediya, v. 13, 2009, 472–473
2008
50.
F. Caruso, J. Eisert, V. Giovannetti, A. S. Holevo, “Multi-mode bosonic Gaussian channels”, New J. Phys., 10 (2008), 083030 , 33 pp. (cited: 45) (cited: 48)
51.
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)
52.
A. S. Holevo, “Entanglement-Breaking Channels in Infinite Dimensions”, Problems Inform. Transmission, 44:3 (2008), 171–184 (cited: 48) (cited: 38) (cited: 38) (cited: 58)
53.
M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90 (cited: 16) (cited: 8) (cited: 8) (cited: 17)
54.
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
55.
A. S. Holevo, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11 (cited: 54) (cited: 42) (cited: 42) (cited: 55)
2006
56.
A. S. Holevo, “The additivity problem in quantum information theory”, International Congress of Mathematicians, Vol. III, Eur. Math. Soc., Zürich, 2006, 999–1018 (cited: 11)
57.
N. Datta, M. Fukuda, A. S. Holevo, “Complementarity and additivity for covariant channels”, Quantum Inf. Process., 5:3 (2006), 179–207 (cited: 6) (cited: 16) (cited: 10) (cited: 17)
58.
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: 58) (cited: 58)
59.
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: 9) (cited: 3) (cited: 3) (cited: 9)
2007
60.
A. S. Holevo, “Complementary channels and the additivity problem”, Theory Probab. Appl., 51:1 (2007), 92–100 (cited: 26) (cited: 13) (cited: 13) (cited: 16)
2006
61.
A. S. Holevo, “Locating a photon:position observables and an uncertainty relation”, Russian Microelectronics, 35:1 (2006), 21–30
62.
N. Datta, A. S. Holevo, Yu. M. Suhov, “Additivity for transpose depolarizing channels”, Int. J. Quant. Inform.,, 4:1 (2006), 85–98 (cited: 7) (cited: 4) (cited: 7)
63.
A. S. Holevo, “Quantum channels: classical capacity”, Encyclopedia of Mathematical Physics, Academic Press, 2006, 142–144
2005
64.
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: 12) (cited: 23)
65.
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: 5)
66.
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: 28) (cited: 22) (cited: 22) (cited: 23)
67.
A. S. Holevo, “The additivity problem and constrained quantum channels”, Proc. Int. Soc. Opt. Eng., 5833 (2005), 196-201
68.
A. S. Holevo, “Additivity conjecture and covariant channels”, Int. J. Quant., 3:1 (2005), 41-48 (cited: 16) (cited: 12) (cited: 17)
2004
69.
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: 26) (cited: 29) (cited: 27)
70.
A. S. Holevo, M. E. Shirokov, “The additivity problem for constrained quantum channels”, Russian Math. Surveys, 59:2 (2004), 385–387
2005
71.
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: 5)
2003
72.
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
73.
A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, 2-e izd., Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003 , 410 pp.
74.
A. S. Kholevo, Statisticheskaya struktura kvantovoi teorii, Institut kompyuternykh issledovanii, Izhevsk, 2003
2004
75.
A. S. Holevo, “Entanglement-assisted capacities of constrained quantum channels”, Theory Probab. Appl., 48:2 (2004), 243–255 (cited: 8) (cited: 13) (cited: 17)
2003
76.
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: 12) (cited: 2) (cited: 2)
2004
77.
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
78.
A. S. Holevo, “On states, channels, and purification”, Quantum Inf. Process., 1:1-2 (2002), 1–4 (cited: 1) (cited: 1)
79.
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: 39) (cited: 85) (cited: 82) (cited: 91)
80.
A. S. Holevo, “On entanglement-assisted classical capacity”, Quantum information theory, J. Math. Phys., 43, no. 9, 2002, 4326–4333 (cited: 14) (cited: 45) (cited: 49)
81.
A. S. Kholevo, Vvedenie v kvantovuyu teoriyu informatsii, MTsNMO, M., 2002 , 128 pp.
2003
82.
G. G. Amosov, A. S. Holevo, “On the multiplicativity hypothesis for quantum communication channels”, Theory Probab. Appl., 47:1 (2003), 123–127 (cited: 9) (cited: 6) (cited: 8)
2002
83.
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
84.
A. S. Holevo, Statistical structure of quantum theory, Lecture Notes in Physics. Monographs, 67, Springer-Verlag, Berlin, 2001 , x+159 pp. (cited: 67)
85.
A. S. Holevo, “Coding theorems of quantum information theory”, XIIIth International Congress on Mathematical Physics (London, 2000), Int. Press, Boston, MA, 2001, 415–422
86.
A. S. Holevo, “Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory”, Math. Methods Statist., 10:1 (2001), 6–22
87.
A. S. Holevo, “An invitation to quantum estimation”, Math. Methods Statist., 10:1 (2001), 1–5
88.
A. S. Holevo, “Lévy processes and continuous quantum measurements”, Lévy processes, Birkhäuser Boston, Boston, MA, 2001, 225–239 (cited: 1)
89.
A. S. Holevo, R. F. Werner, “Evaluating capacities of Bosonic Gaussian channels”, Phys. Rev. A, 63 (2001), 032312 , 13 pp. (cited: 257) (cited: 79)
2000
90.
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: 9) (cited: 9) (cited: 11)
91.
A. S. Holevo, “Reliability function of general classical-quantum channel”, IEEE Trans. Inform. Theory, 46:6 (2000), 2256–2261 (cited: 10) (cited: 27) (cited: 17) (cited: 30)
92.
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
93.
A. S. Holevo, M. Sohma, O. Hirota, “The capacity of quantum Gaussian channels”, Phys. Rev. A, 59:3 (1999), 1820–1828 (cited: 148) (cited: 135) (cited: 151)
94.
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
95.
M. V. Burnashev, A. S. Holevo, “Letter to the Editor”, Problems Inform. Transmission, 35:1 (1999), 93–94
1998
96.
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
97.
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)
98.
A. S. Holevo, “Radon-Nikodým derivatives of quantum instruments”, J. Math. Phys., 39:3 (1998), 1373–1387 (cited: 11) (cited: 23) (cited: 21) (cited: 23)
99.
A. S. Holevo, “The capacity of the quantum channel with general signal states”, IEEE Trans. Inform. Theory, 44:1 (1998), 269–273 (cited: 109) (cited: 594) (cited: 539) (cited: 653)
100.
A. S. Holevo, “Quantum coding theorems”, Russian Math. Surveys, 53:6 (1998), 1295–1331 (cited: 105) (cited: 66) (cited: 109)
101.
M. V. Burnashev, A. S. Holevo, “On the Reliability Function for a Quantum Communication Channel”, Problems Inform. Transmission, 34:2 (1998), 97–107
1999
102.
A. S. Holevo, “International symposium on information theory 1998”, Theory Probab. Appl., 43:4 (1999), 685–686
1997
103.
M. V. Burnashev, A. S. Holevo, On reliability function of quantum communication channel, 1997 , 8 pp., arXiv: quant-ph/9703013
104.
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
105.
A. S. Holevo, “The structure of classical noise”, Analysis, geometry and probability, Texts Read. Math., 10, Hindustan Book Agency, Delhi, 1996, 73–86
106.
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)
107.
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: 8)
108.
A. S. Holevo, “On dissipative stochastic equations in a Hilbert space”, Probab. Theory Related Fields, 104:4 (1996), 483–500 (cited: 14) (cited: 34) (cited: 29) (cited: 33)
109.
A. S. Holevo, “Covariant quantum Markovian evolutions”, J. Math. Phys., 37:4 (1996), 1812–1832 (cited: 7) (cited: 40) (cited: 40)
110.
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: 17)
111.
A. S. Holevo, “There exists a non-standard dynamical semigroup on $\mathfrak L(\mathscr H)$”, Russian Math. Surveys, 51:6 (1996), 1206–1207 (cited: 2)
112.
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
113.
A. Barchielli, A. S. Holevo, “Constructing quantum measurement processes via classical stochastic calculus”, Stochastic Process. Appl., 58:2 (1995), 293–317 (cited: 17) (cited: 46) (cited: 19) (cited: 46)
114.
A. S. Holevo, “On the structure of covariant dynamical semigroups”, J. Funct. Anal., 131:2 (1995), 255–278 (cited: 3) (cited: 22) (cited: 17)
115.
A. S. Holevo, “On translation-covariant quantum Markov equations”, Izv. Math., 59:2 (1995), 427–443 (cited: 17)
116.
A. S. Holevo, “Excessive maps, “arrival times” and perturbation of dynamical semigroups”, Izv. Math., 59:6 (1995), 1311–1325 (cited: 2)
1993
117.
A. S. Holevo, “A note on covariant dynamical semigroups”, Rep. Math. Phys., 32:2 (1993), 211–216 (cited: 9) (cited: 10) (cited: 41)
118.
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: 23)
119.
A. S. Kholevo, “Structure of covariant dynamical semigroups”, Russian Acad. Sci. Dokl. Math., 47:1 (1993), 161–167
120.
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: 9)
121.
A. S. Kholevo, “On the Lévy–Khinchin formula in noncommutative probability theory”, Theory Probab. Appl., 38:4 (1993), 660–672
122.
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)
123.
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
124.
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
125.
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: 19)
126.
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)
127.
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
128.
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
129.
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
130.
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)
1991
131.
A. S. Holevo, “Conditionally positive-definite functions in quantum probability theory”, J. Soviet Math., 56:5 (1991), 2670–2697
132.
A. S. Holevo, “A quantum stochastic calculus”, J. Soviet Math., 56:5 (1991), 2609–2624 (cited: 20)
1992
133.
A. S. Holevo, “Stochastic representations of quantum dynamical semi-groups”, Proc. Steklov Inst. Math., 191 (1992), 145–154
1988
134.
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)
135.
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
136.
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
137.
A. S. Holevo, “Lévy–Khintchine Representation in Quantum Theory of Probability”, Theory Probab. Appl., 32:1 (1987), 131–136 (cited: 5)
138.
A. S. Holevo, “Quantum estimation”, Adv. Statist. Signal Proc., v. 1, JAI Press Inc., 1987, 157–202
139.
A. S. Kholevo, “On a generalization of canonical quantization”, Math. USSR-Izv., 28:1 (1987), 175–188
140.
A. S. Holevo, “Infinite-divisible instruments in quantum probability theory”, Theory Probab. Appl., 31:3 (1987), 493–497 (cited: 2)
1985
141.
A. S. Holevo, “Statistical definition of observable and the structure of statistical models”, Rep. Math. Phys., 22:3 (1985), 385–407 (cited: 3) (cited: 14)
142.
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.
143.
A. S. Holevo, “On the principle of quantum nondemolition measurements”, Theoret. and Math. Phys., 65:3 (1985), 1250–1255 (cited: 1) (cited: 5)
1984
144.
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: 29)
1983
145.
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)
146.
N. A. Bogomolov, A. S. Kholevo, “A characterization of the covariant resolutions of the identity”, Funct. Anal. Appl., 17:2 (1983), 131–132
147.
A. S. Holevo, “Generalized imprimitivity systems for abelian groups”, Soviet Math. (Iz. VUZ), 27:2 (1983), 53–80
148.
A. S. Holevo, “On measurements of the parameters of a quantum random process”, Theoret. and Math. Phys., 57:3 (1983), 1238–1247
1982
149.
A. S. Holevo, “Testing statistical hypotheses in quantum theory”, Probab. Math. Statist., 3:1 (1982), 113–126 (1983) (cited: 1)
150.
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: 140)
151.
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
152.
H. A. Bogomolov, A. S. Kholevo, “Razlozheniya edinitsy, kovariantnye otnositelno predstavleniya abelevoi lokalno kompaktnoi gruppy”, Tr. NIVTs MGU, M., 1981, 45–59
1980
153.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Nauka, Moscow, 1980 , 320 pp.
1979
154.
A. S. Holevo, “Covariant measurements and uncertainty relations”, Rep. Math. Phys., 16:3 (1979), 385–400 (cited: 15) (cited: 16) (cited: 55)
155.
A. S. Holevo, “On Capacity of a Quantum Communications Channel”, Problems Inform. Transmission, 15:4 (1979), 247–253 (cited: 67)
1978
156.
A. S. Holevo, “Estimation of shift parameters of a quantum state”, Rep. Math. Phys., 13:3 (1978), 379–399 (cited: 3) (cited: 40)
1979
157.
N. P. Rasulov, A. S. Holevo, “A regression problem for continuous time series”, Theory Probab. Appl., 22:4 (1979), 731–740 (cited: 1)
158.
A. S. Holevo, “On asymptotically optimal hypotheses testing in quantum statistics”, Theory Probab. Appl., 23:2 (1979), 411–415 (cited: 12)
159.
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
160.
A. S. Holevo, “Commutation superoperator of a state and its applications to the noncommutative statistics”, Rep. Mathematical Phys., 12:2 (1977), 251–271 (cited: 4)
161.
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: 48)
1978
162.
A. S. Kholevo, “Investigations in the general theory of statistical decisions”, Proc. Steklov Inst. Math., 124 (1978), 1–140
1976
163.
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
164.
A. S. Kholevo, “Optimalnoe izmerenie amplitud kompleksnykh signalov na fone kvantovogo shuma”, Trudy 4-go Mezhdunarodnogo simpoziuma po teorii informatsii, Leningrad, 1976
1981
165.
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
166.
A. S. Holevo, “On a vector-valued integral in the “noncommutative” statistical decision theory”, J. Multivariate Anal., 5:4 (1975), 462–465
167.
A. S. Holevo, “Some statistical problems for quantum Gaussian states”, IEEE Trans. Information Theory, IT-21:5 (1975), 533–543 (cited: 1) (cited: 31) (cited: 30)
168.
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
169.
A. S. Kholevo, “The theory of statistical decisions on an operator algebra”, Sov. Math. Dokl., 15 (1974), 1276–1281 (1975)
170.
A. S. Kholevo, “Optimal measurement of the mean value of a Gaussian state”, Engrg. Cybernetics, 12:5 (1974), 128–130
171.
A. S. Holevo, “Remarks on Optimal Quantum Measurements”, Problems Inform. Transmission, 10:4 (1974), 317–320
1973
172.
A. S. Holevo, “On the general problem of mean estimation”, J. Multivariate Anal., 3 (1973), 262–275 (cited: 1)
173.
A. S. Holevo, “Statistical decision theory for quantum systems”, J. Multivariate Anal., 3 (1973), 337–394 (cited: 40) (cited: 48) (cited: 287)
174.
A. S. Holevo, “A Generalization of the Rao–Cramér Inequality”, Theory Probab. Appl., 18:2 (1973), 359–362
175.
A. S. Holevo, “Information-Theoretical Aspects of Quantum Measurement”, Problems Inform. Transmission, 9:2 (1973), 110–118
176.
A. S. Holevo, “Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel”, Problems Inform. Transmission, 9:3 (1973), 177–183
177.
A. S. Holevo, “Optimal quantum measurements”, Theoret. and Math. Phys., 17:3 (1973), 1172–1177 (cited: 3)
178.
A. S. Holevo, “On the quasiequivalence of quasifree states on the $C^*$-algebra of CAR”, Theoret. and Math. Phys., 14:2 (1973), 107–111
179.
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
180.
A. S. Holevo, “An analogue of statistical decision theory and noncommutative probability theory”, Trudy Moskov. Mat. Obšč., 26, 1972, 133–149
1973
181.
A. S. Kholevo, “On estimating functions of the mean”, Theory Probab. Appl., 17:3 (1973), 543–547
182.
A. S. Kholevo, “Some statistical problems for quantum fields”, Theory Probab. Appl., 17:2 (1973), 347–351
1972
183.
A. S. Holevo, “On the Mathematical Theory of Quantum Communication Channels”, Problems Inform. Transmission, 8:1 (1972), 47–54
184.
A. S. Holevo, “On quasiequivalence of locally normal states”, Theoret. and Math. Phys., 13:2 (1972), 1071–1082 (cited: 11)
1971
185.
A. S. Holevo, “Quasifree states of the $C^*$ algebra of CCR. II”, Theoret. and Math. Phys., 6:2 (1971), 103–107 (cited: 2)
186.
A. S. Holevo, “Quasi-free states on the $C^*$ algebra of CCR”, Theoret. and Math. Phys., 6:1 (1971), 1–12 (cited: 2)
187.
A. S. Holevo, “On asymptotic normality of estimates of regression coefficients”, Theory Probab. Appl., 16:4 (1971), 707–711
188.
A. S. Holevo, “On asymptotic efficiency of pseudo-best estimators”, Theory Probab. Appl., 16:3 (1971), 516–527
189.
A. S. Holevo, “Almost periodic signal estimations”, Theory Probab. Appl., 16:2 (1971), 249–263
1970
190.
A. S. Holevo, “Quantum Characteristic Functions”, Problems Inform. Transmission, 6:4 (1970), 316–321
1969
191.
A. S. Holevo, “On estimates of regression coefficients”, Theory Probab. Appl., 4:1 (1969), 79–104
1967
192.
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
193.
A. S. Kholevo, “On Sequential Estimates of Parameters”, Theory Probab. Appl., 12:1 (1967), 147–152
1965
194.
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
195.
A. S. Holevo, “Automata which predict a random process”, Soviet Physics Dokl., 10 (1965), 816–818
Presentations in Math-Net.Ru
1.
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
2018
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