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

We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial…

We study a Mach-Zehnder interferometer fed by a coherent state in one input port and vacuum in the other. We explore a Bayesian phase estimation strategy to demonstrate that it is possible to achieve the standard quantum limit independently…

We present a continuous-time probabilistic approach for estimating the chirp signal and its instantaneous frequency function when the true forms of these functions are not accessible. Our model represents these functions by non-linearly…

This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…

We address phase-shift estimation by means of squeezed vacuum probe and homodyne detection. We analyze Bayesian estimator, which is known to asymptotically saturate the classical Cramer-Rao bound to the variance, and discuss convergence…

We investigate phase and frequency estimation with different measurement strategies under the effect of collective phase noise. First, we consider the standard linear estimation scheme and present an experimentally realisable optimization…

Optimal phase estimation protocols require complex state preparation and readout schemes, generally unavailable or unscalable in many quantum platforms. We develop and analyze a scheme that achieves near-optimal precision up to a constant…

We place limits on semiclassical fluctuations that might be present in the primordial perturbation spectrum. These can arise if some signatures of pre-inflationary features survive the expansion, or could be created by whatever mechanism…

In interferometry, sub-Heisenberg strategies claim to achieve a phase estimation error smaller than the inverse of the mean number of photons employed (Heisenberg bound). Here we show that one can achieve a comparable precision without…

A major obstacle to attain the fundamental precision limit of the phase estimation in an interferometry is the identification and implementation of the optimal measurement. Here we demonstrate that this can be accomplished by the use of…

To find the Hermitian phase operatorof a single-mode electromagnetic field in quantum mechanics, the Schroedinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The…

Phase measurement using a lossless Mach-Zehnder interferometer with certain entangled $N$-photon states can lead to a phase sensitivity of the order of 1/N, the Heisenberg limit. However, previously considered output measurement schemes are…

In this letter, we show that for all the so-called path-symmetric states, the measurement of parity of photon number at the output of an optical interferometer achieves maximal phase sensitivity at the quantum Cramer-Rao bound. Such optimal…

We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic…

We study the problem of estimating the phase shift due to the general relativistic time dilation in the interference of photons using a non-linear Mach-Zender interferometer setup. By introducing two non-linear Kerr materials, one in the…

A statistical algorithm for estimating the characteristic parameter $\alpha$ of the stable law is presented and the estimate of its quadratic deviation is obtained in the paper. This algorithm is applied in the description of the…

Detection of radiation signals is at the heart of precision metrology and sensing. In this article we show how the fluctuations in photon counting signals can be exploited to optimally extract information about the physical parameters that…

The quantum speed limit is a fundamental upper bound on the speed of quantum evolution. However, the actual mathematical expression of this fundamental limit depends on the choice of a measure of distinguishability of quantum states. We…

Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of $\mathcal{O}(1/n)$, where $n$ is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron.…

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…