Related papers: Fundamental precision bounds for three-dimensional…
Recent works identified resolution limits for the distance between incoherent point sources. However, it remains unclear how to choose suitable observables and estimators to reach these limits in practical situations. Here, we show how…
We experimentally demonstrate optomechanical motion and force measurements near the quantum precision limits set by the quantum Cram\'er-Rao bounds (QCRBs). Optical beams in coherent and phase-squeezed states are used to measure the motion…
We analyze the fundamental quantum limit of the resolution of an optical imaging system from the perspective of the detection problem of deciding whether the optical field in the image plane is generated by one incoherent on-axis source…
In this paper we study the joint determination of source and background flux for point sources as observed by digital array detectors. We explicitly compute the two-dimensional Cram\'er-Rao absolute lower bound (CRLB) as well as the…
Localization of a non-cooperative target with binary detectors is considered. A general expression for the Fisher information for estimation of target location and power is developed. This general expression is then used to derive…
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…
The precise determination of the position of point-like emitters and scatterers using far-field optical imaging techniques is of utmost importance for a wide range of applications in medicine, biology, astronomy, and physics. Although the…
We derive a vector generalization of the curvature-corrected Cram\'er--Rao bound (CRB) in the nonasymptotic regime using a Hilbert space square-root embedding. Building on previous scalar results, we establish a \emph{directional} curvature…
In modern radar systems, precise target localization using azimuth and velocity estimation is paramount. Traditional unbiased estimation methods have utilized gradient descent algorithms to reach the theoretical limits of the Cramer Rao…
Optimal measurement scheme with an efficient data processing is important in quantum-enhanced interferometry. Here we prove that for a general binary outcome measurement, the simplest data processing based on inverting the average signal…
The quantum Cram\'er-Rao bound (QCRB) provides an ultimate precision limit allowed by quantum mechanics in parameter estimation. Given any quantum state dependent on a single parameter, there is always a positive-operator valued measurement…
We demonstrate a method to determine the position of single atoms in a three-dimensional optical lattice. Atoms are sparsely loaded from a far-off-resonant optical tweezer into a few vertical planes of a cubic optical lattice positioned…
The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…
The attainability of the quantum Cram\'er-Rao bound [QCR], the ultimate limit in the precision of the estimation of a physical parameter, requires the saturation of the quantum information bound [QIB]. This occurs when the Fisher…
Although direct position estimation (DPE) has been demonstrated to offer enhanced robustness in GNSS receivers, its theoretical limits and performance in OFDM based positioning systems remain largely unexplored. In this paper, the…
We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with…
For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available.…
By using a systematic optimization approach we determine quantum states of light with definite photon number leading to the best possible precision in optical two mode interferometry. Our treatment takes into account the experimentally…
First discovered by Ernest Abbe in 1873, the resolution limit of a far-field microscope is considered determined by the numerical aperture and wavelength of light, approximately $\lambda$/2NA. With the advent of modern fluorescence…
Nonlinear quantum metrology schemes can lead to faster than Heisenberg limited scalings for the measurement uncertainty. We study a Michelson interferometer embedded in a Kerr medium [Luis and Rivas, Phys. Rev. A 92, 022104 (2015)] that…