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Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum…

The Cram\'er-Rao bound captures completely the performance of single-parameter quantum sensors. On the other hand, its extension to multiple parameters demands more caution. Different aspects need to be captured at once, including,…

We implement an estimator for determining the separation between two incoherent point sources. This estimator relies on image inversion interferometry and when used with the appropriate data analytics, it yields an estimate of the…

Resolving the separation between two incoherent optical sources with high precision is of great significance for fluorescence imaging and astronomical observations. In this paper, we focus on a more general scenario where two sources have…

Quantum information science currently poses a troubling contradiction. It can be summarized as: (1) To factor efficiently, quantum computers must perform exponentially precise energy estimation. (2) Exponentially precise energy estimation…

We derive fundamental per-channel bounds on angle-integrated absorption and thermal radiation for arbitrary bodies---for any given material susceptibility and bounding region---that simultaneously encode both the per-volume limit on…

Motivated by the importance of optical microscopes to science and engineering, scientists have pondered for centuries how to improve their resolution and the existence of fundamental resolution limits. In recent years, a new class of…

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…

In quantum metrology, it is widely believed that the quantum Cramer-Rao bound is attainable bound while it is not true. In order to clarify this point, we explain why the quantum Cramer-Rao bound cannot be attained geometrically. In this…

Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a…

In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…

Interferometric methods have been recently investigated to achieve sub-Rayleigh imaging and precision measurements of faint incoherent sources up to the ultimate quantum limit. Here we consider single-photon imaging of two point-like…

A novel interferometric method - SLIVER (Super Localization by Image inVERsion interferometry) - is proposed for estimating the separation of two incoherent point sources with a mean squared error that does not deteriorate as the sources…

The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…

Spectroscopy has an illustrious history delivering serendipitous discoveries and providing a stringent testbed for new physical predictions, including applications from trace materials detection, to understanding the atmospheres of stars…

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…

We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement…

To investigate the fundamental limit to far-field incoherent imaging, the prequels to this work [M. Tsang, Phys. Rev. A 99, 012305 (2019); 104, 052411 (2021)] have studied a quantum lower bound on the error of estimating an object moment…

Quantum Mechanics places limits on achievable transverse beam spot sizes of particle accelerators. We estimate this limit for a linear collider to be \Delta x > \hbar c f/E\delta_0 where f is the final focal length, E the beam energy, and…

The quantum Fisher information matrix (QFIM) is central to multiparameter quantum metrology, dictating the attainable sensitivity via the quantum Cram\'er-Rao bound. In this work, we investigate the ultimate precision limits for…