Related papers: Variational Limits for Phase Precision in Linear Q…
Quantum metrology promises greater sensitivity for optical phase measurements than could ever be achieved classically. Here we present a theory of the phase sensitivity for the general case where the detection probability is given by an $N$…
We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to…
We propose to use weak measurements away from the weak-value amplification regime to carry out precision measurements of time delays of light. Our scheme is robust to several sources of noise that are shown to only limit the relative…
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…
We address the issue of precisely estimating small parameters encoded in a general linear transformation of the modes of a bosonic quantum field. Such Bogoliubov transformations frequently appear in the context of quantum optics. We provide…
We develop a quantum statistical framework for passive optical surface metrology. Modelling a surface as an incoherent ensemble of point emitters imaged through a diffraction-limited system, we employ techniques from quantum parameter…
Quantum noise limits the sensitivity of interferometric measurements. It is generally admitted that it leads to an ultimate sensitivity, the ``standard quantum limit''. Using a semi-classical analysis of quantum noise, we show that a…
Accurate phase estimation plays a pivotal role in quantum metrology, yet its precision is significantly affected by noise, particularly phase-diffusive noise caused by phase drift. To address this challenge, the joint estimation of phase…
We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
We demonstrate accurate phase measurement from low photon level interference data using a constrained optimization method that takes into account the expected redundancy in the unknown phase function. This approach is shown to have…
Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future…
Interferometric phase measurement is widely used to precisely determine quantities such as length, speed, and material properties. Without quantum correlations, the best phase sensitivity $\Delta\varphi$ achievable using $n$ photons is the…
The problem of estimating an unknown phase $ \varphi $ using two-level probes in the presence of unital phase-covariant noise and using finite resources is investigated. We introduce a simple model in which the phase-imprinting operation on…
When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum $1/|\omega|^p$ with $p>1$, then the…
We present a general framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging. This approach can lead to nontrivial bounds of the precision for multiphase…
We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associated optimal state vectors are determined. The probability…
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…
Bounds on the ultimate precision attainable in the estimation of a parameter in Gaussian quantum metrology are obtained when the average number of bosonic probes is fixed. We identify the optimal input probe state among generic (mixed in…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…