Related papers: High Precision Multi-parameter Weak Measurement wi…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ``technical'' instruments and more recently from the empirical strategy of ``judge design''. This paper surveys and…
Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
We study the possibility of varying the measured lifetime of a decaying particle based on the technique of weak value amplification in which an additional filtering process called postselection is performed. Our analysis made in a direct…
We present a framework for simultaneously estimating all four real parameters of a general two-channel unitary U(2) with Heisenberg-scaling precision. We derive analytical expressions for the quantum Fisher information matrix and show that…
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…
The precise measurement of spatial attitude parameters is critical for applications in inertial navigation, industrial monitoring, instrument calibration, quantum metrology, etc. In this work, we theoretically investigate and experimentally…
We discuss the recently introduced concept of non-deterministic noiseless linear amplification, demonstrating that such an operation can only be performed perfectly with vanishing probability of success. We show that a weak measurement,…
As the minituarization of electronic devices, which are sensitive to temperature, grows apace, sensing of temperature with ever smaller probes is more important than ever. Genuinely quantum mechanical schemes of thermometry are thus…
High-precision surface roughness estimation plays an important role in many applications. However, the classical estimating methods are limited by shot noise and only can achieve the precision of 0.1 nm with white light interferometer.…
We describe a weak value inspired phase amplification technique in a Sagnac interferometer. We monitor the relative phase between two paths of a slightly misaligned interferometer by measuring the average position of a split-Gaussian mode…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
This paper introduces a numerical scheme for time harmonic Maxwell's equations by using weak Galerkin (WG) finite element methods. The WG finite element method is based on two operators: discrete weak curl and discrete weak gradient, with…
Due to the reduced probability of successful post-selection, the weak-value amplification seems to be unavailable for the parameter-estimation. Here, we show theoretically that, some effects due to the weak interactions present only in the…
Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe…
Numerical integration methods are central to the study of self-gravitating systems, particularly those comprised of many bodies or otherwise beyond the reach of analytical methods. Predictor-corrector schemes, both multi-step methods and…
The feedback particle filter (FPF) is a promising nonlinear filtering (NLF) method, but its practical implementation is hindered by the intractability of the gain function, which satisfies a boundary value problem (BVP). This paper proposes…
A new weak Galerkin (WG) finite element method for solving the biharmonic equation in two or three dimensional spaces by using polynomials of reduced order is introduced and analyzed. The WG method is on the use of weak functions and their…
Quantum theory allows direct measurement of the average of a non-Hermitian operator using the weak value of the positive semidefinite part of the non-Hermitian operator. Here, we experimentally demonstrate the measurement of weak value and…