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We consider the quantum (trajectories) filtering equation for the case when the system is driven by Bose field inputs prepared in an arbitrary non-zero mean Gaussian state. The a posteriori evolution of the system is conditioned by the results of a single or double homodyne measurements. The system interacting with the Bose field is a single cavity mode taken initially in a Gaussian state. We show explicit solutions using the method of characteristic functions to the filtering equations exploiting the linear Gaussian nature of the problem.
We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace preserving maps. These dynamics going beyond the Lindblad paradigm are obtained with reference to classical renewal proc
The interaction between matter and squeezed light has mostly been treated within the approximation that the field correlation time is small. Methods for treating squeezed light with more general correlations currently involve explicitly modeling the
We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of correlated matr
Simple, controllable models play an important role to learn how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum
Here we deal in a pedagogical way with an approach to construct an algebraic structure for the Quantum Mechanical measurement processes from the concept of emph{Measurement Symbol}. Such concept was conceived by Julian S. Schwinger and constitutes a