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Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In…

Quantum Physics · Physics 2019-09-09 Hiroyasu Tajima , Hiroshi Nagaoka

The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable…

Statistics Theory · Mathematics 2009-09-29 Zvika Ben-Haim , Yonina C. Eldar

Advanced super-resolution imaging techniques require specific approaches for accurate and consistent estimation of the achievable spatial resolution. Fisher information supplied to Cramer-Rao bound (CRB) has proved to be a powerful and…

The thermodynamic uncertainty relation is an inequality stating that it is impossible to attain higher precision than the bound defined by entropy production. In statistical inference theory, information inequalities assert that it is…

Statistical Mechanics · Physics 2019-06-26 Yoshihiko Hasegawa , Tan Van Vu

Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum…

Quantum Physics · Physics 2024-09-11 Kaito Wada , Kazuma Fukuchi , Naoki Yamamoto

The quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a…

Quantum Physics · Physics 2017-08-09 Haixing Miao , Rana X Adhikari , Yiqiu Ma , Belinda Pang , Yanbei Chen

To any parametric family of states of a finite level quantum system we associate a space of Fisher maps and introduce the natural notions of Cram\'er-Rao-Bhattacharya tensor and Fisher information form. This leads us to an abstract…

Probability · Mathematics 2009-07-14 K. R. Parthasarathy

We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate `null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state.…

Quantum Physics · Physics 2023-10-11 Federico Girotti , Alfred Godley , Mădălin Guţă

We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…

Quantum Physics · Physics 2017-06-08 Marco G. Genoni

A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…

Quantum Physics · Physics 2022-04-01 Jaeha Lee

Quantum Fisher information (QFI) is an important feature for the precision of quantum parameter estimation based on the quantum Cram\'er-Rao inequality. When the quantum state satisfies the von Neumann-Landau equation, the local quantum…

Quantum Physics · Physics 2018-02-27 Shao-xiong Wu , Yang Zhang , Chang-shui Yu

This post is the author's doctoral dissertation back in 1997. The dissertation covers following four kinds of problems: First, it studies achievable Cramer-Rao type bounds of various multi-parameter pure state models. Second, it relates…

Quantum Physics · Physics 2021-11-19 Keiji Matsumoto

The Bayesian Cram\'er-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed…

Signal Processing · Electrical Eng. & Systems 2025-02-11 Hai Victor Habi , Hagit Messer , Yoram Bresler

We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean-square errors when estimating relevant parameters with separable…

Quantum Physics · Physics 2016-03-29 Jun Suzuki

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 Physics · Physics 2019-03-20 Aaron Z. Goldberg , Daniel F. V. James

We formulate multiparameter quantum estimation in the parametric and semiparametric setting. While the Holevo Cram\'er-Rao bound (CRB) requires no substantial modifications in moving from the former to the latter, we generalize the Helstrom…

Quantum Physics · Physics 2020-08-10 Francesco Albarelli , Mankei Tsang , Animesh Datta

The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity…

Quantum Physics · Physics 2021-07-14 Zixin Huang , Cosmo Lupo , Pieter Kok

Quantum-enhanced phase estimation paves the way to ultra-precision sensing and is of great realistic significance. In this paper we investigate theoretically the estimation of a second-order nonlinear phase shift using a coherent state and…

Quantum Physics · Physics 2019-02-13 Jian-Dong Zhang , Zi-Jing Zhang , Long-Zhu Cen , Jun-Yan Hu , Yuan Zhao

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed…

Quantum Physics · Physics 2020-03-27 Jing Liu , Haidong Yuan , Xiao-Ming Lu , Xiaoguang Wang

Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows…

Quantum Physics · Physics 2015-06-26 E. Bagan , M. A. Ballester , R. Munoz-Tapia , O. Romero-Isart