English
Related papers

Related papers: Quantum Cram\'er-Rao bound for quantum statistical…

200 papers

This paper studies semiparametric Fisher information in models parametrized by general normed spaces. The main contribution is to establish that positive semiparametric Fisher information is equivalent to the gradient of the parameter of…

Statistics Theory · Mathematics 2026-04-02 Telmo Pérez-Izquierdo

In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection…

Machine Learning · Statistics 2025-11-26 William Hao-Cheng Huang

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…

Quantum Physics · Physics 2016-08-24 Xiao-Ming Lu , Mankei Tsang

We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic…

Quantum Physics · Physics 2018-07-18 Rosanna Nichols , Pietro Liuzzo-Scorpo , Paul A. Knott , Gerardo Adesso

We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of…

Statistics Theory · Mathematics 2017-07-21 Jürgen Jost , Hông Vân Lê , Lorenz Schwachhöfer

As a method to extract information from optical system, imaging can be viewed as a parameter estimation problem. The fundamental precision in locating one emitter or estimating the separation between two incoherent emitters is bounded below…

Quantum Physics · Physics 2021-07-29 Ben Wang , Liang Xu , Lijian Zhang

Localization of a non-cooperative target with binary detectors is considered. A general expression for the Fisher information for estimation of target location and power is developed. This general expression is then used to derive…

Information Theory · Computer Science 2014-07-29 Arian Shoari , Alireza Seyedi

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

Symmetry breaking underlies diverse phenomena from phase transitions in condensed matter to fundamental interactions in gauge theories. Despite many proposed indicators, a general quantification of symmetry breaking that is faithful,…

Statistical Mechanics · Physics 2025-09-10 Shion Yamashika , Shimpei Endo , Hiroyasu Tajima

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…

Quantum Physics · Physics 2017-11-15 T. G. Downes , J. R. van Meter , E. Knill , G. J. Milburn , C. M. Caves

The quantum Fisher information matrix provides us with a tool to determine the precision, in any multiparametric estimation protocol, through quantum Cram\'er-Rao bound. In this work, we study simultaneous and individual estimation…

Quantum Physics · Physics 2019-04-17 L. Bakmou , A. Slaoui , M. Daoud , R. Ahl Laamara

In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the…

Quantum Physics · Physics 2020-01-01 Angelo Carollo , Bernardo Spagnolo , Alexander A. Dubkov , Davide Valenti

We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…

Quantum Physics · Physics 2016-05-11 Nan Li , Christopher Ferrie , Jonathan A. Gross , Amir Kalev , Carlton M. Caves

Morozova and Chentsov (Morozova and Chentsov 90) studied Riemannian metrics on the set of probability measures. They showed that, up to a constant factor, the Fisher information is the only Riemannian metric which is monotone under…

Quantum Physics · Physics 2008-05-02 Caleb J O'Loan

We propose an estimation procedure for $d$-dimensional unitary transformations. For $d>2$, the unitary transformations close to the identity are estimated saturating the quantum Cram\'er-Rao bound. For $d=2$, the estimation of all unitary…

Quantum Physics · Physics 2024-07-17 J. Escandón-Monardes , D. Uzcátegui , M. Rivera-Tapia , S. P. Walborn , A. Delgado

Understanding how well future cosmological experiments can reconstruct the mechanism that generated primordial inhomogeneities is key to assessing the extent to which cosmology can inform fundamental physics. In this work, we apply a…

Cosmology and Nongalactic Astrophysics · Physics 2026-02-23 Michał Piotrak , Thomas Colas , Ana Alonso-Serrano , Alessio Serafini

We develop a quantum metrological framework for resonant nanophotonic sensors based on subwavelength Fabry--Perot slit cavities. Building on classical Fisher-information analyses of resonant transmission sensors, we model parameter encoding…

Quantum Physics · Physics 2025-12-18 J. Sumaya-Martinez

Measurement estimation bounds for local quantum multiparameter estimation, which provide lower bounds on possible measurement uncertainties, have so far been formulated in two ways: by extending the classical Cram\'er--Rao bound (e.g., the…

Quantum Physics · Physics 2024-09-23 Simon K. Yung , Lorcan O. Conlon , Jie Zhao , Ping Koy Lam , Syed M. Assad

This lecture note addresses the common misconception that the Gaussian distribution always yields the largest Cram\'er-Rao Bound (CRB). We show that this property only holds under restrictive conditions: specifically, when the mean and…

Signal Processing · Electrical Eng. & Systems 2026-04-09 Jean-Pierre Delmas , Habti Abeida

We investigate a symmetric logarithmic derivative (SLD) Fisher information for kinetic uncertainty relations (KURs) of open quantum systems described by the GKSL quantum master equation with and without the detailed balance condition. In a…

Statistical Mechanics · Physics 2023-11-30 Satoshi Nakajima , Yasuhiro Utsumi