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We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…

Quantum Physics · Physics 2012-07-11 Vittorio Giovannetti , Seth Lloyd , Lorenzo Maccone

A wide variety of imaging systems have been designed to measure phase variations, with applications from physics to biology and medicine. In this work, we theoretically compare the precision of phase estimations achievable with classical…

Optics · Physics 2021-05-21 Dorian Bouchet , Jonathan Dong , Dante Maestre , Thomas Juffmann

A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we…

Quantum Physics · Physics 2020-03-24 Jesús Rubio , Jacob Dunningham

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well-understood despite it being a…

This paper focusses on the sparse estimation in the situation where both the the sensing matrix and the measurement vector are corrupted by additive Gaussian noises. The performance bound of sparse estimation is analyzed and discussed in…

Information Theory · Computer Science 2015-06-12 Yujie Tang , Laming Chen , Yuantao Gu

Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are…

Quantum Physics · Physics 2019-09-11 Jonas Helsen , Joel J. Wallman , Steven T. Flammia , Stephanie Wehner

We address the problem of existence of unbiased constrained parameter estimators. We show that if the constrained set of parameters is compact and the hypothesized distributions are absolutely continuous with respect to one another, then…

Statistics Theory · Mathematics 2016-09-26 Anelia Somekh-Baruch , Amir Leshem , Venkatesh Saligrama

The paper derives the theoretical Cramer-Rao lower bound for parameter estimation of a source (of emitting energy, gas, aerosol), monitored by a network of sensors providing binary measurements. The theoretical bound is studied in the…

Applications · Statistics 2014-05-30 Branko Ristic , Ajith Gunatilaka , Ralph Gailis

We show that the quantum Cram\'er-Rao bound on the precision of measurements of the optical phase gradient, or the wavefront tilt, with a beam of finite width is consistent with the Heisenberg uncertainty principle for a single-photon…

Quantum Physics · Physics 2020-07-22 Walker Larson , Bahaa E. A. Saleh

One key aspect of quantum metrology, measurement incompatibility, is evident only through the simultaneous estimation of multiple parameters. The symmetric logarithmic derivative Cram\'er-Rao bound (SLDCRB), gives the attainable precision,…

Quantum Physics · Physics 2024-09-26 Lorcán O. Conlon , Jun Suzuki , Ping Koy Lam , Syed M. Assad

Determining when the multiparameter quantum Cram\'er--Rao bound (QCRB) is saturable with experimentally relevant single-copy measurements is a central open problem in quantum metrology. Here we establish an equivalence between QCRB…

Quantum Physics · Physics 2026-01-30 Jing Yang , Satoya Imai , Luca Pezzè

In many estimation theory and statistical analysis problems, the true data model is unknown, or partially unknown. To describe the model generating the data, parameterized models of some degree are used. A question that arises is which…

Signal Processing · Electrical Eng. & Systems 2025-04-08 Nadav E. Rosenthal , Joseph Tabrikian

This work is devoted to solve the problem of estimating the carrier frequency offset, phase offset, amplitude, and SNR between two mmWave transceivers. The Cram\'{e}r-Rao Lower Bound (CRLB) for the different parameters is provided first, as…

Information Theory · Computer Science 2017-12-19 Javier Rodríguez-Fernández , Nuria González-Prelcic , Robert W. Heath

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…

Quantum Physics · Physics 2019-09-19 Manuel Gessner

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…

We address the characterization of qubit chains and assess the performances of local measurements compared to those provided by Feynman probes, i.e. nonlocal measurements realized by coupling a single qubit regis- ter to the chain. We show…

Quantum Physics · Physics 2016-11-17 D. Tamascelli , C. Benedetti , S. Olivares , M. G. A. Paris

In multiparameter quantum metrology, the weighted-arithmetic-mean error of estimation is often used as a scalar cost function to be minimized during design optimization. However, other types of mean error can reveal different facets of…

Quantum Physics · Physics 2020-02-12 Xiao-Ming Lu , Zhihao Ma , Chengjie Zhang

Hard-threshold estimators are popular in signal processing applications. We provide a detailed study of using hard-threshold estimators for estimating an unknown deterministic signal when additive white Gaussian noise corrupts observations.…

Statistics Theory · Mathematics 2008-01-24 Baris I. Erkmen , Vivek K. Goyal

We discuss the Heisenberg limit in the multiparameter metrology within two different paradigms -- the one, where the measurement is repeated many times (so the Cram\'er-Rao bound is guaranteed to be asymptotically saturable) and the second…

Quantum Physics · Physics 2022-09-16 Wojciech Górecki , Rafał Demkowicz-Dobrzański

This paper studies a near-field multiple-input multiple-output (MIMO) radar sensing system, in which the transceivers with massive antennas aim to localize multiple near-field targets in the three-dimensional (3D) space over unknown…

Information Theory · Computer Science 2023-08-31 Haocheng Hua , Jie Xu , Yonina C. Eldar