Related papers: Parameter Estimation for Jump-Diffusion Stochastic…

Accurate quantum channel parameter estimation is essential for effective information reconciliation in continuous-variable quantum key distribution (CV-QKD). However, conventional maximum likelihood (ML) estimators rely on a large amount of…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

The design and analysis of diffusive molecular communication systems generally requires knowledge of the environment's physical and chemical properties. Furthermore, prospective applications might rely on the timely detection of changes in…

In this paper, we consider the problem of distributed parameter estimation in sensor networks. Each sensor makes successive observations of an unknown $d$-dimensional parameter, which might be subject to Gaussian random noises. They aim to…

We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of…

We discuss how continuous probing of a quantum system allows estimation of unknown classical parameters embodied in the Hamiltonian of the system. We generalize the stochastic master equation associated with continuous observation processes…

Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…

Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…

Squeezing a quantum state along a specific direction has long been recognized as a crucial technique for enhancing the precision of quantum metrology by reducing parameter uncertainty. However, practical quantum metrology often involves the…

We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…

This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…

We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…

It is shown how the phase-damping master equation, either in Markovian and nonMarkovian regimes, can be obtained as an averaged random unitary evolution. This, apart from offering a common mathematical setup for both regimes, enables us to…

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…

Reducing computational scaling for simulating non-Markovian dissipative dynamics using artificial neural networks is both a major focus and formidable challenge in open quantum systems. To enable neural quantum states (NQSs), we encode…

We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the…

Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of…

We consider structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. The quasi-likelihood estimators for parameters in the SEM are proposed. The goodness-of-fit test is derived from the…

We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine…

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…