Related papers: On quantum Stochastic Master equations
A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic…
"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…
This paper investigates parameter estimation for open quantum systems under continuous observation, whose conditional dynamics are governed by jump-diffusion stochastic master equations (SMEs) associated with quantum nondemolition (QND)…
We develop a new approach for solving stochastic quantum master equations with mixed initial states. First, we obtain that the solution of the jump-diffusion stochastic master equation is represented by a mixture of pure states satisfying a…
A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative…
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
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…
We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a…
Mean-field stochastic differential equations, also called McKean--Vlasov equations, are the limiting equations of interacting particle systems with fully symmetric interaction potential. Such systems play an important role in a variety of…
Quantum master equations are an invaluable tool to model the dynamics of a plethora of microscopic systems, ranging from quantum optics and quantum information processing, to energy and charge transport, electronic and nuclear spin…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…
We consider an open quantum many-particle system in which there are dissipative processes. The evolution of this system is described by a kinetic equation for the density matrix. From the equation describing a random Markov process in this…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…
We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schr\"odinger…
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…