Viacheslav Belavkin

Viacheslav Belavkin's AcademicInfluence.com Rankings

Viacheslav Belavkin

Mathematics

#3417

World Rank

#5045

Historical Rank

Measure Theory

#2528

World Rank

#3034

Historical Rank

mathematics Degrees

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Mathematics

Why Is Viacheslav Belavkin Influential?

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According to Wikipedia, Viacheslav Pavlovich Belavkin was a Russian-British professor in applied mathematics at the University of Nottingham. An active researcher, he was one of the pioneers of quantum probability. His research spanned areas such as quantum filtering, quantum information and quantum chaos.

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Viacheslav Belavkin's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Quantum stochastic calculus and quantum nonlinear filtering (1992) (331)
Measurements continuous in time and a posteriori states in quantum mechanics (1991) (279)
Quantum continual measurements and a posteriori collapse on CCR (1992) (187)
Nondemolition measurements, nonlinear filtering and dynamic programming of quantum stochastic processes (1989) (151)
A new wave equation for a continuous nondemolition measurement (1989) (146)
Non-Demolition Measurement and Control in Quantum Dynamical Systems (1987) (121)
Measurement, filtering and control in quantum open dynamical systems (1999) (118)
Quantum communications and measurement (1995) (99)
Optimal multiple quantum statistical hypothesis testing (1975) (95)
Quantum Filtering of Markov Signals with White Quantum Noise (2005) (95)
A quantum nonadapted Ito formula and stochastic analysis in Fock scale (1991) (83)
Nondemolition principle of quantum measurement theory (1994) (79)
A posterior Schrödinger equation for continuous nondemolition measurement (1990) (78)
A continuous counting observation and posterior quantum dynamics (1989) (77)
THEORY OF THE CONTROL OF OBSERVABLE QUANTUM SYSTEMS (2005) (76)
C*-algebraic generalization of relative entropy and entropy (1982) (74)
A quantum particle undergoing continuous observation (1989) (70)
Bellman equations for optimal feedback control of qubit states (2004) (62)
Optimal Quantum Filtering and Quantum Feedback Control (2005) (60)
Quantum Diffusion, Measurement and Filtering I (1994) (56)
Operational distance and fidelity for quantum channels (2004) (52)
Quantum Stochastic Positive Evolutions:¶Characterization, Construction, Dilation (1997) (52)
Generalized uncertainty relations and efficient measurements in quantum systems (1976) (48)
Hamilton-Jacobi-Bellman equations for quantum optimal feedback control (2005) (48)
Chaotic states and stochastic integration in quantum systems (1992) (47)
Quantum Filtering and Optimal Control (2008) (44)
Optimal Measurement and Control in Quantum Dynamical Systems (2005) (41)
A new form and a ⋆-algebraic structure of quantum stochastic integrals in Fock space (1988) (41)
Entanglement, quantum entropy and mutual information (2002) (40)
A stochastic posterior Schrödinger equation for counting nondemolition measurement (1990) (38)
Reconstruction theorem for a quantum stochastic process (1985) (36)
A Radon-Nikodym theorem for completely positive maps (1986) (36)
Optimal Quantum Feedback Control via Quantum Dynamic Programming (2005) (35)
QUANTUM ENTROPY AND INFORMATION IN DISCRETE ENTANGLED STATES (2001) (33)
Optimum distinction of non-orthogonal quantum signals (1975) (32)
Continuous non-demolition observation quantum filtering and optimal estimation (2005) (31)
On a general kinetic equation for many–particle systems with interaction, fragmentation and coagulation (2003) (29)
A stochastic Hamiltonian approach for quantum jumps, spontaneous localizations, and continuous trajectories (1996) (29)
Towards the theory of control in observable quantum systems (2004) (29)
Quantum causality, stochastics, trajectories and information (2002) (21)
Dynamical programming of continuously observed quantum systems (2008) (20)
Quantum entanglements and entangled mutual entropy (1998) (20)
On Quantum Itô Algebras and Their Decompositions (1998) (19)
Stochastic calculus of quantum input-output processes and quantum nondemolition filtering (1991) (18)
A continuous observation of photon emission (1991) (18)
Uniformization method in the theory of Nonlinear Hamiltonian systems of Vlasov and Hartree type (1977) (17)
Eventum Mechanics of Quantum Trajectories: Continual Measurements, Quantum Predictions and Feedback Control (2007) (15)
Discussion on "On quantum statistical inference" by Barndorff-Nielsen, Gill and Jupp (2003) (15)
Stochastic Posterior Equations for Quantum Nonlinear Filtering (1990) (14)
A Dynamical Theory of Quantum Measurement and Spontaneous Localization (2005) (14)
A quantum stochastic calculus in fock space of input and output nondemolition processes (1990) (14)
Quantum control and information processing (2013) (13)
QUANTUM CAUSALITY, DECOHERENCE, TRAJECTORIES AND INFORMATION (2005) (13)
Asymptotic dynamics of a system of a large number of particles described by the Kolmogorov-Feller equations (1981) (13)
Kernel Representations of ☆-semigroups Associated With Infinitely Divisible States (1992) (13)
MATHEMATICAL ASPECTS OF COMPUTER ENGINEERING Advances in Science and Technology in the USSR Design of Optimal Dynamic Analyzers: Mathematical Aspects of Wave Pattern Recognition (2004) (12)
Multiquantum systems and point processes I. Generating functionals and nonlinear semigroups (1989) (12)
FEYNMAN PATH INTEGRAL CORRESPONDING TO THE SCHRODINGER STOCHASTIC EQUATION (1998) (12)
Reconstruction theorem for quantum stochastic processes (2005) (12)
Continuous measurements of quantum phase (1994) (11)
Dynamical interpretation for the quantum-measurement projection postulate (1996) (11)
Quantum stochastic differential equation for unstable systems (2000) (11)
On Entangled Information and Quantum Capacity (2001) (11)
Quantum stochastic Dirac boundary value problem, and the ultrarelativistic limit (2000) (10)
Quantum stochastics and information : statistics, filtering, and control : University of Nottingham, UK, 15-22 July 2006 (2008) (10)
Quantum noise, bits and jumps : uncertainties, decoherence, measurements and filtering (2001) (9)
The unified Ito formula has the pseudo‐Poisson structure df(x)=[f(x+b)−f(x)]μνdaνμ (1993) (9)
Semiclassical asymptotics of quantum stochastic equations (1991) (9)
AN OPERATIONAL ALGEBRAIC APPROACH TO QUANTUM CHANNEL CAPACITY (2008) (9)
A pseudo-euclidean representation of conditionally positive mappings (1991) (8)
Optimization of quantum observation and control (1980) (8)
POSITIVE DEFINITE GERMS OF QUANTUM STOCHASTIC PROCESSES (2005) (7)
Stochastic evolutions as boundary value problems (2001) (7)
Monotone quantum stochastic processes and covariant dynamical hemigroups (2011) (7)
The Nondemolition Measurement of Quantum Time (2005) (7)
Information Divergence for Quantum Channels (2006) (7)
On Stochastic Generators of Completely Positive Cocycles (2005) (7)
On Entangled Quantum Capacity (2002) (7)
ENTANGLEMENTS AND COMPOUND STATES IN QUANTUM INFORMATION THEORY (2000) (7)
Quantum Stochastics, Dirac Boundary Value Problem, and the Ultra Relativistic Limit (2005) (6)
Quantum quasi-Markov processes in eventum mechanics dynamics, observation, filtering and control (2013) (6)
Contravariant densities, complete distancesand relative fidelities for quantum channels* (2004) (6)
Noncommutative dynamics and generalized master equations (2010) (6)
The World of Quantum Noise and the Fundamental Output Process (1995) (5)
Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrodinger equations (2002) (5)
Quantum Trajectories, State Diffusion, and Time-Asymmetric Eventum Mechanics (2003) (5)
Conditional entropy in algebraic statistical physics (1984) (5)
Infinite Dimensional Ito Algebras of Quantum White Noise (2005) (5)
Optimization of Quantum Information Processing Maximizing Mutual Information (2005) (5)
Quantum Probabilities and Paradoxes of the Quantum Century (2000) (5)
QUANTUM ITÔ ALGEBRAS: AXIOMS, REPRESENTATIONS, DECOMPOSITIONS (2003) (4)
THE KERNEL OF A FOCK SPACE OPERATOR II (1993) (4)
Quantum Ito B*-algebras, their Classification and Decomposition (2005) (4)
RECONSTRUCTION THEOREM FOR STATIONARY MONOTONE QUANTUM MARKOV PROCESSES (2012) (4)
The interplay of classical and quantum stochastics: Diffusion, measurement and filtering (1995) (4)
Q-Adapted Quantum Stochastic Integrals and Differentials in Fock Scale (2011) (4)
ON THE EQUIVALENCE OF QUANTUM STOCHASTICS AND A DIRAC BOUNDARY VALUE PROBLEM, AND AN INDUCTIVE STOCHASTIC LIMIT (New Development of Infinite-Dimensional Analysis and Quantum Probability) (2000) (3)
Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space (2011) (3)
Dynamical Solution to the Quantum Measurement Problem, Causality, and Paradoxes of the Quantum Century (2000) (3)
Quantum demolition filtering and optimal control of unstable systems (2012) (3)
Quantum Noise, Bits and Jumps: Uncertainties, Decoherence, Trajectories and Filtering (2005) (3)
ON THE DYNAMICAL SOLUTION OF QUANTUM MEASUREMENT PROBLEM (2005) (2)
THE QUANTUM FUNCTIONAL ITO FORMULA HAS THE PSEUDO-POISSON STRUCTURE $df(X) = [f(X+B)-f(X)]^{\mu}_{\nu}dA^{\nu}_{\mu}$ (1993) (2)
A Hamiltonian Solution to Quantum Collapse, State Diffusion and Spontaneous Localization (1995) (2)
On the General Form of Quantum Stochastic Evolution Equation (2005) (2)
A boson field stochastic calculus and quantum filtering in Fock space (1989) (2)
Measurement and Filtering of Quantum Diffusion II (1995) (2)
New Types of Quantum Entropies and Additive Information Capacities (2011) (2)
Quantum noise, bits, jumps: uncertainties, decoherence, measurements and filterings (2001) (2)
ADDITIVITY OF ENTANGLED CHANNEL CAPACITY GIVEN QUANTUM INPUT STATES (2008) (2)
Quantum Filtering and Control in Example: Unstable Qubits (2009) (2)
Notes on the equality in SSA of entropy on CAR algebra (2006) (1)
Quantum Lévy–Itô algebras and non-commutative stochastic analysis (2012) (1)
Stochastic Evolutions As Boundary Value Problems (Infinite Dimensional Analysis and Quantum Probability Theory) (2001) (1)
Contravariant Densities, Operational Distances and Quantum Channel Fidelities (2004) (1)
QUANTUM SEX AND MUTUAL INFORMATION (Infinite Dimensional Analysis and Quantum Probability Theory) (2001) (1)
COVARIANT QUANTUM STOCHASTIC FLOWS AND THEIR DILATION (2007) (1)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: A reconstruction theorem for a quantized random field (1984) (1)
On Stochastic Generators of Positive Definite Exponents (2005) (1)
QUANTUM WHITE NOISE ANALYSIS AND QUANTUM STOCHASTIC EQUATIONS (2011) (1)
On the Sufficient Optimality Condition for Quantum Information Processing (2005) (1)
Quantum Probability and Applications (QP-PQ) (2009) (0)
EVENTUM MECHANICS AS THE CROSSROAD OF PROBABILITY, INFINITE-DIMENSIONALITY AND NON-COMMUTATIVITY (2003) (0)
Special issue on quantum control and information processing (2013) (0)
On Classification of Quantum Entangled States (量子情報と量子カオスの数理) (2000) (0)
A Game Theoretic Approach to Quantum Information (2007) (0)
Fe b 20 07 Additivity of Entangled Channel Capacity for Quantum Input States (2007) (0)
Quantum stochastic semigroups and their generators (2005) (0)
Quantum quasi-Markov processes in eventum mechanics dynamics, observation, filtering and control (2012) (0)
On the Generators of Quantum Stochastic Master Equation (2005) (0)
On Stochastic Schrödinger Equation as a Dirac Boundary-Value Problem, and an Inductive Stochastic Limit (2005) (0)
A ug 2 00 5 Optimal Quantum Filtering and Quantum Feedback Control (2005) (0)
Optimization of Quantum Information Processing at Mutual Information Criterion (1973) (0)
Stochastic Positive Flows and Quantum Filtering Equations (1998) (0)
TOWARDS QUANTUM CYBERNETICS: OPTIMAL FEEDBACK CONTROL IN QUANTUM BIO INFORMATICS (2009) (0)
Quantum control and information processing (2012) (0)
Quantum proper entropies and additive capacities of quantum information channels (2011) (0)
Noncommutative dynamics is the unified dynamics of quantum and classical systems on a C *-algebra represented in a Hilbert space Γ with a generating state vector (2010) (0)
Aspects of a representation of quantum theory in terms of classical probability theory by means of integration in Hilbert space (2016) (0)
Stochastic Model of a Quantum Diffusion-Reaction Process (1994) (0)
Representations of homogeneous quantum Lévy fields (2006) (0)
Special issue on quantum control and information processing (2012) (0)
Semilogics, Quasilogics and Other Quantum Structures (2005) (0)
Quantum Itô algebra and quantum martingale (2007) (0)
MULTIPLE Q -ADAPTED INTEGRALS AND IT ^ O FORMULA OF NONCOMMUTATIVE STOCHASTIC CALCULUS (2012) (0)
ON CLASSIFICATION OF QUANTUM ENTANGLED STATES (Mathematical Aspects of Quantum Information and Quantum Chaos) (2000) (0)
QUANTUM CAUSALITY AND QUANTUM CONTROL: A MODEL, DUALITY AND AXIOMS(Micro-Macro Duality in Quantum Analysis) (2007) (0)
ec 2 00 5 SEMILOGICS , QUASILOGICS AND OTHER QUANTUM STRUCTURES (0)
ov 2 00 5 Optimization of Quantum Information Processing Maximizing the Mutual Information ∗ (1973) (0)
QUANTUM FILTERING AND OPTIMAL FEEDBACK CONTROL OF A GAUSSIAN QUANTUM FREE PARTICLE (2006) (0)
Uniformization of Nonlinear Hamiltonian Systems of Vlasov and Hartree Type (2005) (0)
Quantum quasi-Markov processes, L-dynamics, and noncommutative Girsanov transformation (2010) (0)
A nonadapted stochastic calculus and non stationary evolution in Fock scale (2005) (0)
A posterior stochastic equation for quantum Brownian motion (1989) (0)
ec 2 00 5 Quantum Stochastic Differential Equation for Unstable Systems (2000) (0)
MULTIQUANTUM MARKOV SEMIGROUPS, INTERACTING BRANCHING PROCESSES AND NONLINEAR KINETIC EQUATIONS. FINITE DIMENSIONAL CASE. (2005) (0)
Towards Quantum ɛ—Entropy and Validity of Quantum Information (1993) (0)
On Quantum Stochastic Differential Equations as Dirac Boundary-Value Problems (2001) (0)

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