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Nanomechanical resonators can now be realized that achieve fundamental resonance frequencies exceeding 1 GHz, with quality factors (Q) in the range 1,000 - 100,000. The minuscule active masses of these devices, in conjunction with their…

Precise measurements of tiny forces and displacements play an important role in science and technology. The precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is necessarily spoiled by the…

We determine the quantum Cram\'er-Rao bound for the precision with which the oscillator frequency and damping constant of a damped quantum harmonic oscillator in an arbitrary Gaussian state can be estimated. This goes beyond standard…

We determine the quantum mechanical limits to inertial mass-sensing based on nanomechanical systems. We first consider a harmonically oscillating cantilever whose vibration frequency is changed by mass accretion at its surface. We show that…

Nanomechanical oscillators are at the heart of ultrasensitive detectors of force, mass and motion. As these detectors progress to even better sensitivity, they will encounter measurement limits imposed by the laws of quantum mechanics. For…

We determine the bound to the maximum achievable sensitivity in the estimation of a scalar parameter from the information contained in an optical image in the presence of quantum noise. This limit, based on the Cramer-Rao bound, is valid…

We show that the detection sensitivity of a linear detector is lower bounded by some quantum limits. For the force detection, relevant for atomic force microscopes, the lower bound is given by the so-called ultimate quantum limit. For the…

We address the problem of estimating the mass of a quantum particle in a gravitational field and seek the ultimate bounds to precision of quantum-limited detection schemes. In particular, we study the effect of the field on the achievable…

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…

The quantum Cram\'er-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a…

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…

We derive a quantum Cram\'er-Rao bound (QCRB) on the error of estimating a time-changing signal. The QCRB provides a fundamental limit to the performance of general quantum sensors, such as gravitational-wave detectors, force sensors, and…

In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…

Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting qubits close to the quantum regime and to measure their properties with an accuracy close to the Heisenberg…

Mechanical systems are ideal candidates for studying quantumbehavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently,…

Many protocols require precise rotation measurement. Here we present a general class of states that surpass the shot noise limit for measuring rotation around arbitrary axes. We then derive a quantum Cram\'er-Rao bound for simultaneously…

Quantum sensors hold considerable promise for precision measurement, yet their capabilities are inherently constrained by environmental noise. A fundamental task in quantum sensing is determining the precision limit of noisy sensor devices.…

The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical…

A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…

The observation of quantum phenomena in macroscopic mechanical oscillators has been a subject of interest since the inception of quantum mechanics. Prerequisite to this regime are both preparation of the mechanical oscillator at low phonon…