Quantum covariance and filtering

Sampled-data filtering with error covariance assignment

In this correspondence, we consider the sampled-data filtering problem by proposing a new performance criterion in terms of the estimation error covariance. An innovation approach to sampled-data filtering is presented. First, the definition of the estimation covariance for a sampled-data system is given, then the sampled-data filtering problem is reduced to the Kalman filter design problem for...

Optimal Quantum Filtering and Quantum Feedback Control

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 is then applied to the explicitly solv...

Quantum Stochastic Calculus and Quantum Nonlinear Filtering

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 calculus, and the problem of QS nonlinear …lt...

General Covariance in Quantum Gravity

The question of general covariance in quantum gravity is considered in the first post-Newtonian approximation. Transformation properties of observable quantities under deformations of a reference frame, induced by variations of the gauge conditions fixing general invariance, are determined. It is found that the one-loop contributions violate the principle of general covariance, in the sense tha...

Covariance Approach to Quantum Theory