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219
Belavkin Filtering with Squeezed Light Sources
"... We derive the filtering equation for Markovian systems undergoing homodyne measurement in the situation where the output processes being monitored are squeezed. The filtering theory applies to case where the system is driven by Fock noise (that, quantum input processes in a coherent state) and whe ..."
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the filtered estimate pit(a) for the mode annihilator a based on the homodyne quadrature observations up to time t. In memory of Slava Belavkin. 1
BELAVKIN–KOLOKOLTSOV WATCH–DOG EFFECTS IN INTERACTIVELY CONTROLLED STOCHASTIC COMPUTERGRAPHIC DYNAMICAL SYSTEMS. A SUMMARY OF MATHEMATICAL RESEARCHES.
, 1994
"... Abstract. This paper contains a summary of mathematical researches of stochastic properties of the long time behavior of a continuously observed (and interactively controlled) quantum–field top. Applications to interactively controlled stochastic computergraphic dynamical systems are also discussed ..."
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Cited by 2 (2 self)
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Abstract. This paper contains a summary of mathematical researches of stochastic properties of the long time behavior of a continuously observed (and interactively controlled) quantum–field top. Applications to interactively controlled stochastic computergraphic dynamical systems are also
An introduction to quantum filtering
, 2006
"... This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a ..."
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Cited by 77 (19 self)
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This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a
Quantum Stochastic Calculus and Quantum Nonlinear Filtering
 J.Multivariate Analysis
, 1992
"... Abstract. A ⋆–algebraic indefinite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an infinitely dimensional nuclear space. The class of nondemolition output QS proces ..."
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Cited by 99 (19 self)
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general quantum filtering stochastic equation for a QS process is derived. An application to the description of the spontaneous collapse of the quantum spin under continuous observation is given.
Quantum filtering: a reference probability approach
, 2005
"... These notes are intended as an introduction to noncommutative (quantum) filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as the least squares estimate, and culminating in the construction of Wiener and Poisson ..."
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Cited by 9 (1 self)
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processes on the Fock space. Next we describe the HudsonParthasarathy quantum Itô calculus and its use in the modelling of physical systems. Finally, we use a reference probability method to obtain quantum filtering equations, in the BelavkinZakai (unnormalized) form, for several systemobservation models
Stochastic Schrödinger equations
 J. PHYS. A: MATH. GEN
"... A derivation of stochastic Schrödinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the system: it is possible to keep track in real time of the best es ..."
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Cited by 46 (8 self)
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A derivation of stochastic Schrödinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the system: it is possible to keep track in real time of the best
HamiltonJacobiBellman equations for Quantum Filtering and Control
, 2005
"... We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding HamiltonJacobiBellman equations using the elementary arguments of classical contr ..."
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Cited by 9 (3 self)
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We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding HamiltonJacobiBellman equations using the elementary arguments of classical
Optimal Quantum Filtering and . . .
, 2005
"... Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic control theory, we present the theory of nonlinear optimal quantu ..."
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quantum feedback control. The resulting quantum Bellman equation is then applied to the explicitly solvable quantum linearquadraticGaussian (LQG) problem which emphasizes many similarities with the corresponding classical control problem.
Results 1  10
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219