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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 inde-terministic control theory, we present the theory of nonlinear optimal quantum feedback control. The resulting quantum Bellman equation… (More)

The operational structure of quantum couplings and entangle-ments is studied and classified for semifinite von Neumann algebras. We show that the classical-quantum correspondences such as quantum encodings can be treated as diagonal semi-classical (d-) couplings, and the entanglements characterized by truly quantum (q-) couplings, can be regarded as truly… (More)

We develop a rigorous treatment of discontinuous stochastic unitary evolution for a system of quantum particles that interacts singularly with quantum " bubbles " at random instants of time. This model of a " cloud chamber " allows to watch and follow with a quantum particle trajectory like in cloud chamber by sequential unsharp localization of spontaneous… (More)

- V P Belavkin
- 1992

A quantum theory for the Markovian dynamics of an open system under the unsharp observation which is continuous in time, is developed within the CCR stochastic approach. A stochastic classical equation for the posterior evolution of quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave… (More)

- V P Belavkin
- 1989

A stochastic model for nondemolition continuous measurement in a quantum system is given. It is shown that the posterior dynamics, including a continuous collapse of the wave function, is described by a non-linear stochastic wave equation. For a particle in an electromagnetic field it reduces the Schrödinger equation with extra imaginary stochastic… (More)

- V P Belavkin, P Staszewski
- 1991

A stochastic model of a continuous nondemolition observation of a free quantum Brownian motion is presented. The nonlinear stochastic wave equation describing the posterior dynamics of the observed quantum system is solved in a Gaussian case for a free particle of mass m > 0. It is shown that the dispersion of the wave packet does not increase to infinity… (More)

- Luc Bouten, G J Heckman Copromotor, J D M Maassen, V P Belavkin, R D Gill, B Kümmerer
- 2004

Acknowledgments The theme for this thesis, applying the tools of quantum probability to problems in quantum optics, was provided by Hans Maassen, who has been my supervisor for the past four years. Apart from sharing his deep insight in quantum mechanics, I am grateful to Hans for his patience and encouragement in finding my own way in research. I would… (More)

Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct ob-servability continual case. Quantum theory of time continuous measurements and quantum prediction theory, developed by the author on the basis of an independent-increment model for quantum noise and nondemolition… (More)

The pure quantum entanglement is generalized to the case of mixed compound states on an operator algebra to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized by quantum couplings which are described as transpose-CP, but not Completely Positive (CP), trace-normalized linear positive maps of the… (More)

- V P Belavkin
- 1980

Time-continuous non-anticipating quantum processes of nonde-molition measurements are introduced as the dynamical realizations of the causal quasi-measurements, which are described in this paper by the adapted operator-valued probability measures on the trajectory spaces of the generalized temporal observations in quantum open systems. In particular, the… (More)