Related papers: Quantum-Limited Estimation of Phase Gradient
The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing…
Multiparameter quantum estimation theory is crucial for many applications involving infinite-dimensional Gaussian quantum systems, since they can describe many physical platforms, e.g., quantum optical and optomechanical systems and atomic…
We experimentally analyzed the statistical errors in quantum-state estimation and examined whether their lower bound, which is derived from the Cramer-Rao inequality, can be truly attained or not. In the experiments, polarization states of…
We propose quantum versions of the Bell-Ziv-Zakai lower bounds on the error in multiparameter estimation. As an application we consider measurement of a time-varying optical phase signal with stationary Gaussian prior statistics and a power…
Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a ``mode parameter'' that determines properties such as…
Optical magnetometers use the rotation of linearly polarized laser light induced by the Faraday effect for high precision magnetic field measurements. Here, we carry out an in-depth quantum information investigation, deploying two distinct…
Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase…
The Cram\'{e}r-Rao bound plays a central role in both classical and quantum parameter estimation, but finding the observable and the resulting inversion estimator that saturates this bound remains an open issue for general multi-outcome…
We demonstrate the ultimate sensitivity allowed by quantum physics in the estimation of the time delay between two photons by measuring their interference at a beam-splitter through frequency-resolving sampling measurements. This…
The quantum Cram\'er-Rao (QCR) bound sets the ultimate local precision limit for unbiased multiparameter estimation. Yet, unlike in the single-parameter case, its saturability is not generally guaranteed and is often assessed through…
The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general limit beyond…
Modern precision measurements, such as interferometry for detecting gravitational waves, rely on the estimation of optical phases encoded in light fields. Here, we propose to exploit the collectively enhanced output field of a…
Quantum metrology protocols are typically designed around the assumption that we have an abundance of measurement data, but recent practical applications are increasingly driving interest in cases with very limited data. In this regime the…
Phase diffusion invariably accompanies all phase estimation strategies -- quantum or classical. A precise estimation of the former can often provide valuable understanding of the physics of the phase generating phenomena itself. We…
Quantum phase estimation is an important component in diverse quantum algorithms. However, it suffers from spectral leakage, when the reciprocal of the record length is not an integer multiple of the unknown phase, which incurs an accuracy…
Shaping single-mode operation in high-power fibres requires a precise knowledge of the gain-medium optical properties. This requires accurate measurements of the refractive index differences ($\Delta$n) between the core and the cladding of…
I propose classical and quantum limits to the statistical resolution of two incoherent optical point sources from the perspective of minimax parameter estimation. Unlike earlier results based on the Cram\'er-Rao bound, the limits proposed…
The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed…
We consider the problem of quantum phase estimation with access to arbitrary measurements in a single suboptimal basis. The achievable sensitivity limit in this case is determined by the classical Cram\'{e}r-Rao bound with respect to the…
Wavefront distortions are a leading source of systematic uncertainty in light-pulse atom interferometry, limiting absolute measurements of gravitational acceleration at the 30 nm/s$^2$ level. Here, we demonstrate in situ spatially resolved…