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A ?algebraic inde
nite 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 in
nitely dimensional nuclear space. The class of nondemolition output QS processes in quantum open systems is characterized in terms of the QS… (More)

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)

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 nonlinear stochastic wave equation. For a particle in an electromagnetic field it reduces the Schrödinger equation with extra imaginary stochastic… (More)

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 vector… (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)

Time-continuous non-anticipating quantum processes of nondemolition 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 indeterministic control theory, we present the theory of nonlinear optimal quantum feedback control. The resulting quantum Bellman equation… (More)

Statistically interpretable axioms are formulated that define a quantum stochastic process (QSP) as a causally ordered field in an arbitrary space–time region T of an open quantum system under a sequential observation at a discrete space-time localization. It is shown that to every QSP described in the weak sense by a self-consistent system of causally… (More)

We deduce the most general kinetic equation that describe the low density limit of general Feller processes for the systems of random number of particles with interaction, collisions, fragmentation and coagulation. This is done by studying the limiting as ε → 0 evolution of Feller processes on ∪∞n Xn with X = Rd or X = Zd described by the generators of the… (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)