My recent scientific interests are concentrated in the following three directions:
--  Quantum  information, communication and computing;
--  Noncommutative probability theory, quantum and classical stochastic processes, quantum Markov property and dynamical semigroups;
--  Statistical structure of quantum theory, quantum measurement.
    A list of selected publications in these directions is given below. For earlier publications comprizing, above the three aforementioned topics, statistics of classical random processes, algebraic approach to quantum theory and applied functional analysis, see  the complete    list of publications .  For Arxiv e-prints see
Electronic Archive    or the  mirror site in Moscow.
    Quantum information theory is a rich source of difficult mathematical problems having simple formulation and a profound physical motivation.

            QUANTUM INFORMATION AND COMMUNICATION

Entanglement-breaking channels in infinite dimensions, Problems of Information Transmission, v. 44, n. 3, 3-18, 2008. Arxiv quant-ph/0802.0235

(with M. E. Shirokov) On approximation of infinite-dimensional quantum channels, Problems of Information Transmission, v. 44, n. 2, 3-22, 2008.

(with F. Caruso, J. Eisert, V. Giovannetti) Multi-mode bosonic Gaussian channels, New Journal of Physics 10, 083030 (33 pp) 2008. Arxiv quant-ph/0804.0511

Quantum informatics, World of Science (Russian edition of "Scientific American") N 7, 68-75, 2008.

(with V. Giovannetti) Quantum shared broadcasting, Quant. Inform. Proc. 7, 55-69 2008. Arxiv quant-ph/0802.0235.

One-mode quantum Gaussian channels, Problems of Information Transmission, v.43, 1-11, 2007; Arxiv quant-ph/0607051.

The additivity problem in quantum information theory, Proc. of International Congress of Mathematicians, Madrid, Spain, 2006. vol. 3, pp. 999-1018, Publ. EMS 2006.

Multiplicativity of p-norms of completely positive maps and the additivity problem in quantum information theory, Russian Math. Surveys, vol. 61, N2, 2006, 113-152.

Classical capacity of quantum channels. Encyclopaedia "Mathematical Physics",
Elsevier, Oxford, 2006, 142-144.

(with F. Caruso, V. Giovannetti) One-mode Bosonic Gaussian channels: a full weak-degradability classification, New Journal of Physics 8, 310 (2006); Arxiv quant-ph/0609013.

Photon localization: observables and uncertainty relation, Microelectronics, vol. 35, N1, 2006, 27-36.

On complementary channels and the additivity problem, Arxiv quant-ph/0509101, 2005;
Probab. theory and appl. v. 51, N1, 2006, 133-134.

(with M. E. Shirokov) Continuous ensembles and the capacity of infinite dimensional channels.
Probab. Theory and Appl. v. 50, N1, 2005, 98-114.

(with M. E. Shirokov) Additivity problem for constrained quantum channels. Russian Math. Surveys,
vol. 59, N2, 2004, 195-196.

(with N. Datta and Yu. M. Suhov) A quantum channel with additive minimum output entropy, Arxiv quant-ph/0403072.

Additivity conjecture and covariant channels, Proc. Conference ``Foundations of Quantum Information''', Camerino, 16-19.04.2004.

(with M. E. Shirokov) On Shor's channel extension and constrained channels. Arxiv e-print quant-ph/0306196, 2003.
Commun. Math. Phys. v. 249,
417-430, 2004.

Classical capacities of constrained quantum channel. Probab. theory and appl. v. 48, N2, 2003, 359-374.

Remarks on the classical capacity of quantum channel. Arxiv e-print quant-ph/0212025, 2002. 

Entanglement-assisted capacity of constrained quantum channel. Arxiv e-print quant-ph/0211170, 2002.
   
On states, channels and purification. Arxiv e-print quant-ph/0204077, 2002. Q. Inform. Processing, vol.1, N1, 2002.
    
(with R. F. Werner) Counterexample to an additivity conjecture for output purity of quantum channels.
Arxiv e-print quant-ph/0203003, 2002. J. Math. Phys., vol. 43, N9, 2002, 4353-4357.

On entanglement-assisted classical capacity. Arxiv e-print quant-ph/0106075, 2001. J. Math. Phys., vol. 43, N9, 2002, 4326-4333.

(with G. G. Amosov) On the multiplicativity conjecture for quantum channels.  Arxive-print math-ph/0103015, 2001.
Theor. Probab. Appl. vol. 47, no.1, 2002, 143-146.

Coding theorems of quantum information theory.  Proc. XIII International Congress for Mathematical
  Physics, London, 16-23.07.2000. International Press, Boston, 2001, pp. 415-422.

(with G. G. Amosov and R. F. Werner) On additivity/multiplicativity problems for quantum channels.
 Proc. V-th International Conference on Quantum Communication, Computing and Measurement, Capri,
  03-08.07.2000. Ed. O. Hirota, P. Tombesi. Plenum Press, New York- London.

 (with R. F. Werner) Evaluating capacities of Bosonic Gaussian channels.  Arxive-print quant-ph/9912067,
  1999. Phys. Rev. A. , vol. 63, 2001, 032312.

(with G. G. Amosov and R. F. Werner) On some additivity problems in quantum information theory. Probl. Inform. Transm., vol. 36, N4, 2000. Arxiv e-print quant-ph/0003002.

(with M. Sohma, O. Hirota) Error exponents of quantum channels with constrained inputs. Rep. Math. Phys., vol. 46, N3, 2000, 343-358.

Reliability function of general classical-quantum channel. IEEE Trans. on Information Theory, vol. 46, N6, 2000, 2256-2260. Arxiv e-print quant-ph/9907087, 1999.

(with M. Sohma and O. Hirota) The capacity of quantum Gaussian channels. Phys. Rev. A, vol. 59, N3, 1999, 1820-1828.

Quantum coding theorems. Uspekhi Mat. Nauk, vol. 53, N6, 1998, 193-230 (rus); English translation: Russian Math. Surveys, vol. 53, N6, 1998, 1295-1331.

The capacity of quantum channel with general signal states. Arxiv e-print  quant-ph/9611023, 1996. Appeared in IEEE Trans. Inform. Theory, v. 44, N1, 1998,  269-273.

         QUANTUM AND CLASSICAL STOCHASTIC PROCESSES.
                         NONCOMMUTATIVE PROBABILITY

There exists a non-standard dynamical semigroup on B(H). Uspekhi
Mat. Nauk., v. 51(6), 1996, 225-226 (rus).

Stochastic differential equations in Hilbert space and quantum Markovian evolutions.
In: Probability Theory and Mathematical Statistics. Proc. 7th Japan- Russia
Symp. Tokyo, 26-30.07.1995. Ed. S. Watanabe, M. Fukushima, Yu. V. Prohorov and
A. N. Shiryaev. World Scientific, 1996, 122-131.

Covariant quantum Markovian evolutions. J. Math. Phys., 1996, v.37(4),
1812-1832.

Exponential formulae in quantum stochastic calculus.  Proc. Royal Academy of
Edinbourgh., 1996, v.126A, 375-389.

On dissipative stochastic equations in Hilbert space. Probab.
Theory Rel. Fields,  1996, v.104, 483-500.

Excessive maps, "arrival times" and perturbations of dynamical semigroups.
Izvestiya: Mathematics., 1995, v.59, N6, 207-222 (rus); English translation
- 1311-1325.

On the structure of covariant dynamical semigroups. J. Funct. Anal., 1995,
v.131, 255-278.

On translation-covariant Markovian master equations. Izvestiya: Mathematics,
1995, v.59, N2, 205-221 (rus); English translation - 427-443.

(with A. Barchielli)  Constructing quantum measurement processes via classical
stochastic calculus. Stoch.Proc. and Appl., 1995, v.58, 293-317.

Structure of covariant dynamical semigroups. Russian Acad. Sci. Dokl. Math.,
1993, v.328, N6, 666-670 (rus); English translation - v.47, 161-167.

Stochastic representations of quantum dynamical semigroups. Proc. Steklov
Math. Inst., 1989, v.191, 130-139 (rus); AMS Translation: 1992, Issue 2, 145-154.

Conditionally positive-definite functions in quantum probability. Proc. of
Internat. Congress of Mathematicians, Berkeley, Calif., USA (1986), 1987,
1011-1020.

             STATISTICAL STRUCTURE OF QUANTUM THEORY.
                                QUANTUM MEASUREMENT

Probabilistic and statistical aspects of quantum theory. 2d edition,
corrected and complemented. ICI, Moscow-Izhevsk, 2003. (rus.) 404 p.

Asymptotic estimation of shift parameter of a quantum state, Arxiv quant-ph/0307225, 2003.Probab. theory and appl. v. 49, N2, 2004.

Optimal receiver of a binary coherent signals based on the principle of optical feedback. Laser Physics, vol. 13, N10, 2003, 1-4.
    
Radon-Nikodym derivatives of quantum instruments. J. Math. Phys.,
v. 39, N 3, 1998, 1373-1387.

Quantum measurement. In: Encyclopaedia of Mathematical Physics, Russian Encyclopaedia,
1998, pp. 256-258 (rus).

Quantum probability and quantum statistics. VINITI, Moscow, 1991, v.83, 132p.
(rus).

Statistical inference for quantum processes. Lect. Notes Phys.,1991, v.378,
127-137.

On a generalization of canonical quantization. Izv. Acad. Nauk SSSR, ser. mat.,
1986, v.50, N1, 181-194 (rus); Translation - Math USSR Izvestiya, 1987, v.28,
 N1, 175-188.