相关论文: Stochastic Heisenberg limit: Optimal estimation of…

We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between the…

Squeezed-vacuum twin beams, commonly generated through parametric down-conversion, are known to have perfect photon-number correlations. According to the Heisenberg principle, this is accompanied by a huge uncertainty in their relative…

Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organisation of everyday life. Many biological processes also depend on time estimation by nanoscale clocks,…

A boundary time-crystal is a quantum many-body system whose dynamics is governed by the competition between coherent driving and collective dissipation. It is composed of $N$ two-level systems and features a transition between a stationary…

Light in which the quantum fluctuations have been squeezed is often proposed as a means of obtaining an improved phase reference compared to that available from coherent light. Such a phase reference contains information about the phase of…

In this paper, we report a theoretical study of the phase diffusion in a gain-switched single-mode semiconductor laser. We use stochastic rate equations for the electrical field to analyze the phase statistics of the gain-switched laser.…

Consider the Allen-Cahn equation on the $d$-dimensional torus, $d=2,3$, in the sharp interface limit. As it is well known, the limiting dynamics is described by the motion by mean curvature of the interface between the two stable phases.…

We discuss asymptotics for the boundary of critical Boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter $\alpha \in (1,2)$.…

Recently it has been shown that it is possible for a laser to produce a stationary beam with a coherence (quantified as the mean photon number at spectral peak) which scales as the fourth power of the mean number of excitations stored…

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…

We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The…

The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…

Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum…

Various phase concepts may be treated as special cases of the maximum likelihood estimation. For example the discrete Fourier estimation that actually coincides with the operational phase of Noh, Fouge`res and Mandel is obtained for…

We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide…

Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in…

The quantum fisher information and quantum correlation parameters are employed to study the application of non-classical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state…

When standard light sources are employed, the precision of the phase determination is limited by the shot noise. Quantum entanglement provides means to exceed this limit with the celebrated example of N00N states that saturate the ultimate…

We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cram\'er-Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of…

From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, $\mean{\Delta \hat{q}^2}\mean{\Delta…