Related papers: On stability of continuous-time quantum-filters
The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic…
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 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…
We derive the stochastic master equations, that is to say, quantum filters, and master equations for an arbitrary quantum system probed by a continuous-mode bosonic input field in two types of non-classical states. Specifically, we consider…
The purpose of this paper is to determine quantum master and filter equations for systems coupled to fields in certain non-classical continuous-mode states. Specifically, we consider two types of field states (i) single photon states, and…
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…
We address the question of stability of quantum trajectories, also referred as quantum filters}. We determine the limit of the quantum fidelity between the true quantum trajectory and the {estimated one}. Under a purification assumption we…
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,…
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 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…
The stability of quantum systems to perturbations of the Hamiltonian is studied. This stability is quantified by the fidelity. Dependence of fidelity on the initial state as well as on the dynamical properties of the system is considered.…
We propose and investigate bounds on quantum process fidelity of quantum filters, i.e. probabilistic quantum operations represented by a single Kraus operator K. These bounds generalize the Hofmann bounds on quantum process fidelity of…
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 joint state of a continuously monitored quantum system and the classical filtered measurement record has recently been shown to be described by a quantum Fokker-Planck master equation [Phys. Rev. Lett. 129, 050401 (2022)]. We present a…
The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the…
We investigated the quantum state of an optomechanical suspended mirror under continuous measurement and feedback control using Wiener filtering. We focus on the impact of the two-mode theory of suspended mirror on the quantum state, which…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities…
The fidelity and local unitary transformation are two widely useful notions in quantum physics. We study two constrained optimization problems in terms of the maximal and minimal fidelity between two bipartite quantum states undergoing…
We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the…