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Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…

Quantum Physics · Physics 2009-11-07 Denes Petz

We present a toolbox of new techniques and concepts for the efficient forecasting of experimental sensitivities. These are applicable to a large range of scenarios in (astro-)particle physics, and based on the Fisher information formalism.…

Instrumentation and Methods for Astrophysics · Physics 2018-02-28 Thomas D. P. Edwards , Christoph Weniger

There has been considerable recent interest in the mean-field dynamics of various atom-interferometry schemes designed for precision sensing. In the field of quantum metrology, the standard tools for evaluating metrological sensitivity are…

Quantum Physics · Physics 2016-06-13 Simon A. Haine

Quantum metrology is a science about quantum measurements and it plays a key role in precision of quantum parameter estimation. Meanwhile, quantum coherence is an important quantum feature and quantum Fisher information (QFI) is an…

Quantum Physics · Physics 2025-10-30 Jun-Long Zhao , Li Yu , Ming Yang , Chui-Ping Yang

We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states…

Quantum Physics · Physics 2021-11-25 Kok Chuan Tan , Varun Narasimhachar , Bartosz Regula

Fisher information provides a rigorous theoretical benchmark for evaluating quantum sensor sensitivity; however, a comprehensive framework for quantifying the fundamental limits of Rydberg-atom microwave electrometers remains lacking. In…

Optics · Physics 2026-03-04 Chen-Rong Liu , Runxia Tao , Xiang Lv , Ying Dong , Chuang Li , Binbin Wei , Mingti Zhou

The conventional formulation of quantum sensing is based on the assumption that the probe is reset to its initial state after each measurement. In a very distinct approach, one can also pursue a sequential measurement scheme in which…

Quantum Physics · Physics 2023-08-08 Yaoling Yang , Victor Montenegro , Abolfazl Bayat

We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for…

Quantum Physics · Physics 2026-05-25 Francesco Musso , Vittorio Vitale , Sara Murciano

The Quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state, and can be regarded as a reliability measure of a quantum system as a quantum sensor. However, estimation of the QFI for…

Quantum Physics · Physics 2022-02-03 Jacob L. Beckey , M. Cerezo , Akira Sone , Patrick J. Coles

Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…

Quantum Physics · Physics 2009-08-25 Matteo G. A. Paris

We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different…

Quantitative Methods · Quantitative Biology 2025-05-14 Michał Komorowski

The purport of quantum teleportation is to completely transfer information from one party to another distant partner. However, from the perspective of parameter estimation, it is the information carried by a particular parameter, not the…

Quantum Physics · Physics 2022-09-22 Xing Xiao , Yao Yao , Wo-Jun Zhong , Yan-Ling Li , Ying-Mao Xie

The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles…

The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…

Methodology · Statistics 2023-06-06 William R. Coulton , Benjamin D. Wandelt

The goal of quantum metrology is to improve measurements' sensitivities by harnessing quantum resources. Metrologists often aim to maximize the quantum Fisher information, which bounds the measurement setup's sensitivity. In studies of…

The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we…

Quantum Physics · Physics 2021-06-25 M. Cerezo , Akira Sone , Jacob L. Beckey , Patrick J. Coles

By using the quantum Fisher information (QFI), we address the process of \textit{single}-parameter estimation in the presence of bosonic as well as fermionic environments and protection of information against the noise. In particular, the…

Quantum Physics · Physics 2020-09-01 Hossein Rangani Jahromi , Mansoureh Amini , Mohammad Ghanaatian

The estimation of continuous parameters from measured data plays a central role in many fields of physics. A key tool in understanding and improving such estimation processes is the concept of Fisher information, which quantifies how…

We develop a new framework to optimize and understand uncertainty from in situ strong field measurements of laser field parameters. We present the first derivation of quantum and classical Fisher information for an electron undergoing…

Quantum Physics · Physics 2021-08-06 A. S. Maxwell , A. Serafini , S. Bose , C. Figueira de Morisson Faria

Braunstein and Caves (1994) proposed to use Helstrom's {\em quantum information} number to define, meaningfully, a metric on the set of all possible states of a given quantum system. They showed that the quantum information is nothing else…

Quantum Physics · Physics 2009-10-31 O. E. Barndorff-Nielsen , R. D. Gill