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We propose a simple method to estimate the parameters of a continuously measured quantum system, by fitting correlation functions of the measured signal. We demonstrate the approach in simulation, both on toy examples and on a recent…
The knowledge of receiver beam shapes is essential for accurate radio interferometric imaging. Traditionally, this information is obtained by holographic techniques or by numerical simulation. However, such methods are not feasible for an…
This paper explores as didactically as possible the fundamental principles of both classical and quantum metrology, focusing on the Cram\'er-Rao Bound and how it defines the maximum precision in parameter estimation, taking into account…
This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The…
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote…
Distributed aperture telescopes are a well-established approach for boosting resolution in astronomical imaging. However, theoretical limits on quantitative imaging precision, and the fundamentally best possible beam-combining and detection…
In this report we present a general approach for estimating quantum circuits by means of measurements. We apply the developed general approach for estimating the quality of superconducting and optical quantum chips. Using the methods of…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…
Phase estimation is the most investigated protocol in quantum metrology, but its performance is affected by the presence of noise, also in the form of imperfect state preparation. Here we discuss how to address this scenario by using a…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
We study the fundamental bounds on precision measurements of parameters contained in a time-dependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a…
Estimation of parameters is a pivotal task throughout science and technology. Quantum Cram\'{e}r-Rao bound provides a fundamental limit of precision allowed to achieve under quantum theory. For closed quantum systems, it has been shown how…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
Decoherence often happens in the quantum world. We try to utilize quantum dephasing to build an optimal thermometry. By calculating the Cram$\acute{e}$r-Rao bound, we prove that the Ramsey measurement is the optimal way to measure the…
The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on…
We investigate how squeezing techniques can improve the measurement precision in multiphase quantum metrology. While these methods are well-studied and effectively used in single-phase estimations, their usage in multiphase situations has…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
We apply the variational method to obtain the universal and analytical lower bounds for parameter precision in some noisy systems. We first derive a lower bound for phase precision in lossy optical interferometry at non-zero temperature.…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…