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- 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
- 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)

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)

- 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
- 1999

A Markovian model for a quantum automata, i.e. an open quantum dynamical system with input and output channels and a feedback is described. A multi-stage version of the theory of quantum measurement and statistical decisions applied to the optimal control problem for quantum dynamical discrete-time objects is developed. Quantum analogies of Stratonovich… (More)

- V. P. Belavkin
- 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)

- V. P. BELAVKIN
- 2005

We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous– spectrum and continuous-in-time observations. The " collapsed state–vector " after the " objectification " is simply treated as a random… (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)

We describe the quantum filtering dynamics for a diffusive non-demolition measurement on an open quantum system. This is then used to determine appropriate feedback controls for the system and the quantum Bellman equation for optimal quantum feedback control is derived. These equations are demonstrated on the fully solvable model of the multi-dimensional… (More)

- Viacheslav P. Belavkin
- Open Syst. Inform. Dynam.
- 2001

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)