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We investigate simultaneous estimation of multi-parameter quantum estimation with time-dependent Hamiltonians. We analytically obtain the maximal quantum Fisher information matrix for two-parameter in time-dependent three-level systems. The…

Quantum Physics · Physics 2021-09-06 Dong Xie , Chunling Xu

A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form $\theta G$. For such "phase shift Hamiltonians" it has been shown that…

Quantum Physics · Physics 2017-07-05 Julien Mathieu Elias Fraisse , Daniel Braun

The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing…

Quantum Physics · Physics 2025-04-21 Javier Navarro , Ricard Ravell Rodríguez , Mikel Sanz

Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically this increases the quantum Fisher information with respect to…

Quantum Physics · Physics 2024-02-12 Christoph Hotter , Helmut Ritsch , Karol Gietka

The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…

Quantum Physics · Physics 2012-11-21 B. M. Escher , L. Davidovich , N. Zagury , R. L. de Matos Filho

We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…

Information Theory · Computer Science 2016-11-17 Neri Merhav

The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…

Quantum Physics · Physics 2026-02-25 Zixin Huang , Johannes Jakob Meyer , Theshani Nuradha , Mark M. Wilde

Time is a valuable resource and it seems intuitive that longer time should lead to better precision in Hamiltonian parameter estimation. However recent studies have put this intuition into question, showing longer time may even lead to…

Quantum Physics · Physics 2015-09-16 Haidong Yuan , Chi-Hang Fred Fung

Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…

Numerical Analysis · Computer Science 2014-12-04 Uri Ascher , Farbod Roosta-Khorasani

For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained…

Optimization and Control · Mathematics 2022-07-18 Olle Kjellqvist , Anders Rantzer

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm…

Quantum Physics · Physics 2012-10-10 Christopher E. Granade , Christopher Ferrie , Nathan Wiebe , D. G. Cory

We derive ultimate precision bounds for estimating parameters encoded in \emph{time-dependent} Hamiltonians in the presence of general Markovian noise, allowing for arbitrary adaptive protocols with fast controls and noiseless ancillas.…

Quantum Physics · Physics 2026-05-19 Luca Previdi , Francesco Albarelli

This is a technical report that extends and clarifies the results presented in [1]. The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise…

Optimization and Control · Mathematics 2018-09-05 Marco Lauricella , Lorenzo Fagiano

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…

Quantum Physics · Physics 2021-09-15 Aaron Z. Goldberg , Luis L. Sánchez-Soto , Hugo Ferretti

Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task.…

Quantum Physics · Physics 2023-09-12 Shoukang Chang , Wei Ye , Xuan Rao , Huan Zhang , Liqing Huang , Mengmeng Luo , Yuetao Chen , Qiang Ma , Shaoyan Gao

We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for…

Quantum Physics · Physics 2013-05-29 Kevin C. Young , Mohan Sarovar , Robert Kosut , K. Birgitta Whaley

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 propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cram\'er-Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of…

Optics · Physics 2013-10-31 Shan Zheng Ang , Glen I. Harris , Warwick P. Bowen , Mankei Tsang

The classical Cram\'er-Rao inequality gives a lower bound for the variance of a unbiased estimator of an unknown parameter, in some statistical model of a random process. In this note we rewrite the statment and proof of the bound using…

Other Statistics · Statistics 2017-10-27 Anthony D. Blaom

Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between…

Quantum Physics · Physics 2020-03-16 Ilya Kull , Philippe Allard Guérin , Frank Verstraete