Related papers: Observability from measurable sets for strongly co…
We construct a linear optics measurement process to determine the entanglement measure, named \emph{I-concurrence}, of a set of $4 \times 4$ dimensional two-photon entangled pure states produced in the optical parametric down conversion…
The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllabil-ity problem is the main tool. It is based on an explicit expression of a…
This paper is addressed to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators…
The traditional optical concept for the object does not provide an experimental feasibility to speak for itself, due to the fact that no measuring instrument catches up with the fluctuation of light fields. Using the theory of coherence, we…
We propose a scheme to test Bell's inequalities for an arbitrary number of measurement outcomes on entangled continuous variable states. The Bell correlation functions are expressible in terms of phase-space quasiprobability functions with…
We provide a novel criterion for identifying quantum correlation, which allows us to find connections between Bell type inequalities, entanglement detection, and correlation. We utilize the criterion to construct witness operators that can…
This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved;…
Basing on the analogy between the coherent states of light and separable states of $N$ bosons, we demonstrate that the violation Cauchy-Schwarz inequality for any-order correlation function signals the entanglement among the constituent…
Local well-posedness for a nonlinear parabolic-hyperbolic coupled system modelling Micro-Electro-Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has…
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…
We present a method to derive explicit forms of tight correlation function Bell inequalities for three systems and dichotomic observables, which involve three settings for each observer. We also give sufficient conditions for quantum…
Observability inequalities on lattice points are established for non-negative solutions of the heat equation with potentials in the whole space. As applications, some controllability results of heat equations are derived by the…
This paper considers the problem of controlling a piecewise continuously differentiable system subject to time-varying uncertainties. The uncertainties are decomposed into a time-invariant, linearly-parameterized portion and a time-varying…
The purpose of this short note is to show how it is possible to combine existing results in the literature to get the unique continuation from sets of positive measure for time dependent parabolic equations with Lipschitz principal part and…
This work attempts to discuss the observability of linear time-invariant systems with event-triggered measurements. A new notion of observability, namely, $\epsilon$-observability is defined with parameter $\epsilon$, which relates to the…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference $\theta$. Being to a large extent analytically solvable, the model reveals a rich $\theta$ dependence of the…
We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold $\Omega,$ with or without boundary, where the observation (or control) domain is…
Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, non-negative polynomials, the matrix approach, as well…
This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the…