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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)
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)
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)
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)
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)