Quantum filtering in coherent states

Abstract

Abstract. We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are in a general coherent state.

Quantum Control of Optomechanical Systems

“…In this section we derive the stochastic master equation for homodyne detection from the perspective of classical nonlinear filtering. In our derivation we will follow the technique laid out in [GK10]. First we briefly review the most important properties of the conditional expectation value (see, e. g., [BVJ07]).…”

Classical robots perturbed by Lévy processes: analysis and Lévy disturbance rejection methods

“…This idea of constructing a nonlinear dynamical filter can be found in [25]. The quantum non-commutative case discussed in [25] is a generalization of the classical commutative situation which we have discussed here.…”

Posterior quantum dynamics for a continuous diffusion observation of a coherent channel

“…The Belavkin filtering equation was obtained under the assumption that the Bose field modelling the apparatus was initially prepared in the vacuum state. In [8][9][10] this assumption has been relaxed and the filtering equation has been derived for the Bose field prepared in a coherent state for the counting and diffusion observations. The aim of this paper is twofold -we present the Belavkin equation for the diffusion observation with the apparatus prepared initially in a coherent state and we discuss the time development of a squeezed coherent state undergoing a balance heterodyne measurement [11].…”