Related papers: Stability of continuous-time quantum filters with …
We prove that the fidelity between the quantum state governed by a continuous time stochastic master equation driven by a Wiener process and its associated quantum-filter state is a sub-martingale. This result is a generalization to…
This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the…
From the key composite quantum system made of a two-level system (qubit) and a harmonic oscillator (photon) with resonant or dispersive interactions, one derives the corresponding quantum Stochastic Master Equations (SME) when either the…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
During a continuous measurement, quantum systems can be described by a stochastic Schr\"odinger equation which, in the appropriate limit, reproduces the von Neumann wave-function collapse. The average behavior on the ensemble of all…
In this paper, we consider stochastic master equations describing the evolutions of quantum systems interacting with electromagnetic fields undergoing continuous-time measurements. In particular, we study feedback control of quantum…
We derive a formalism of stochastic master equations (SME) which describes the decoherence dynamics of a system in spin environments conditioned on the measurement record. Markovian and non-Markovian nature of environment can be revealed by…
The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. Initial lack of knowledge of the system and external noises are accounted…
Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…
Quantum measurements are crucial to observe the properties of a quantum system, which however unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system while being subject to a…
Wavefunction collapse is commonly associated with unavoidable physical disturbance of the measured system. Here we show that in driven-dissipative quantum systems, continuous measurement can induce strong trajectory-level collapse while…
A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is…
When are quantum filters asymptotically independent of the initial state? We show that this is the case for absolutely continuous initial states when the quantum stochastic model satisfies an observability condition. When the initial system…
the stability criterion is constructed for open quantum systems which govern by quantum stochastic differential equations (QSDE) both for quantum observable flow and the stochastic density operator. We derive stability criteria (local,…
Fidelity is known to increase through any Kraus map: the fidelity between two density matrices is less than the fidelity between their images via a Kraus map. We prove here that, in average, fidelity is also increasing for any discrete-time…
This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
We consider a controlled quantum system whose finite dimensional state is governed by a discrete-time nonlinear Markov process. In open-loop, the measurements are assumed to be quantum non-demolition (QND). The eigenstates of the measured…
We consider several observers who monitor different parts of the environment of a single quantum system and use their data to deduce its state. We derive a set of conditional stochastic master equations that describe the evolution of the…
Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic,…