Related papers: Standard Quantum Limits for broadband position mea…
In Kalman filtering, unknown inputs are often estimated by augmenting the state vector, which introduces reliance on fictitious input models. In contrast, minimum-variance unbiased methods estimate inputs and states separately, avoiding…
The most efficient modern optical communication is known as coherent communication and its standard quantum limit (SQL) is almost reachable with current technology. Though it has been predicted for a long time that this SQL could be…
In a variety of problems, the number and state of multiple moving targets are unknown and are subject to be inferred from their measurements obtained by a sensor with limited sensing ability. This type of problems is raised in a variety of…
Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting and prediction of epidemics. Particle filters are a widely…
In preparation for the era of the time-domain astronomy with upcoming large-scale surveys, we propose a state-space representation of a multivariate damped random walk process as a tool to analyze irregularly-spaced multi-filter light…
We discuss quantum inequalities for minimally coupled scalar fields in static spacetimes. These are inequalities which place limits on the magnitude and duration of negative energy densities. We derive a general expression for the quantum…
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
In this study, we analyze the bound-state energy spectrum of quark-antiquark systems using the semiclassical WKB approximation. We consider the Cornell potential, which combines a linear confinement term with a Coulombic interaction, and…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
We report on a simple strategy to treat mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. Extending the method of counting, introduced in [Lett. Math.…
In this paper, a distributed dual-quaternion multiplicative extended Kalman filter for the estimation of poses and velocities of individual satellites in a fleet of spacecraft is analyzed. The proposed algorithm uses both absolute and…
The purpose of this paper is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper \cite{ZGPG18}. The spectral structure of quantum linear systems is explored, which…
This paper addresses state estimation of linear systems with special attention on unknown process and measurement noise covariances, aiming to enhance estimation accuracy while preserving the stability guarantee of the Kalman filter. To…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…
Recent development in quantum information sciences and technologies, especially building programmable quantum computers, provide us new opportunities to study fundamental aspects of quantum mechanics. We propose qubit models to emulate the…
This paper is concerned with the mathematical analysis of continuous time Ensemble Kalman Filters (EnKBFs) and their mean field limit in an infinite dimensional setting. The signal is determined by a nonlinear Stochastic Partial…
Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe…
Quantum speed limits (QSLs) provide an upper bound for the speed of evolution of quantum states in any physical process. Based on the Stratonovich-Weyl correspondence, we derive a universal QSL bound in arbitrary phase spaces that is…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…