Related papers: Invariant measure for stochastic Schr\"odinger equ…
The evolution of a quantum system undergoing repeated indirect measurements naturally leads to a Markov chain on the set of states which is called a quantum trajectory. In this paper we consider a specific model of such a quantum trajectory…
Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this…
Quantum trajectories are Markov processes describing the evolution of a quantum system subject to indirect measurements. They can be viewed as place dependent iterated function systems or the result of products of dependent and non…
"Quantum trajectories" are solutions of stochastic differential equations of non-usual type. Such equations are called "Belavkin" or "Stochastic Schr\"odinger Equations" and describe random phenomena in continuous measurement theory of Open…
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…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
Quantum measurements are described as instantaneous projections in textbooks. They can be stretched out in time using weak measurements, whereby one can observe the evolution of a quantum state as it heads towards one of the eigenstates of…
Beyond their use as numerical tools, quantum trajectories can be ascribed a degree of reality in terms of quantum measurement theory. In fact, they arise naturally from considering continuous observation of a damped quantum system. A…
In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual type…
We consider the situation of a two-level quantum system undergoing a continuous indirect measurement, giving rise to so-called "quantum trajectories". We first describe these quantum trajectories in a physically realistic discrete-time…
A central feature of quantum mechanics is that a measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system…
In this article we reconsider a version of quantum trajectory theory based on the stochastic Schr\"odinger equation with stochastic coefficients, which was mathematically introduced in the '90s, and we develop it in order to describe the…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum…
Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding…
In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be…
Starting from a generalization of the quantum trajectory theory (based on the stochastic Schr\"odinger equation - SSE), non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in…
We investigate the asymptotic stability and ergodic properties of quantum trajectories under imperfect measurement, extending previous results established for the ideal case of perfect measurement. We establish a necessary and sufficient…
The paper is devoted to the study of nonlinear stochastic Schr\"{o}dinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born--Markov approximations, this…