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Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…

Quantum Physics · Physics 2024-07-25 Wangjun Lu , Zhao-Hui Peng , HongTao

The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…

Statistics Theory · Mathematics 2021-09-24 Antony M. Overstall

We present a unifying variational calculus derivation of Groverian geodesics for both quantum state vectors and quantum probability amplitudes. In the first case, we show that horizontal affinely parametrized geodesic paths on the Hilbert…

Mathematical Physics · Physics 2020-11-16 Carlo Cafaro , Domenico Felice , Paul M. Alsing

Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…

Information Theory · Computer Science 2017-03-14 Alexandre L. M. Levada

The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical r\^{o}le…

High Energy Physics - Theory · Physics 2012-12-04 Diego Julio Cirilo-Lombardo , Victor I. Afonso

We investigate the connection between the time-evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramer-Rao bound, we find that the rate of change of the…

Statistical Mechanics · Physics 2020-07-01 Sosuke Ito , Andreas Dechant

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The…

Quantum Physics · Physics 2015-03-13 Alex Monras , Fabrizio Illuminati

The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…

Statistical Mechanics · Physics 2016-05-04 Omri Har Shemesh , Rick Quax , Alfons G. Hoekstra , Peter M. A. Sloot

Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…

Quantum Physics · Physics 2007-05-23 Piotr Garbaczewski

We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…

Probability · Mathematics 2025-06-25 Masoud Ataei

Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…

Statistics Theory · Mathematics 2026-04-15 Malik Amir , Sourangshu Ghosh

A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change…

Machine Learning · Statistics 2020-05-21 Florent Bouchard , Ammar Mian , Jialun Zhou , Salem Said , Guillaume Ginolhac , Yannick Berthoumieu

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This…

Quantum Physics · Physics 2026-02-13 Yudai Suzuki , Marek Gluza , Jeongrak Son , Bi Hong Tiang , Nelly H. Y. Ng , Zoë Holmes

This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…

Methodology · Statistics 2014-01-13 Sueli I. R. Costa , Sandra A. Santos , João E. Strapasson

We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: i. classical part associated to the Fisher information of the…

Quantum Physics · Physics 2015-04-09 S. Alipour , A. T. Rezakhani

We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate…

Classical Physics · Physics 2023-08-09 Kunal Pal , Kuntal Pal , Tapobrata Sarkar

Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's…

General Relativity and Quantum Cosmology · Physics 2026-05-19 Per Berglund , Andrew Geraci , Tristan Hubsch , David Mattingly , Djordje Minic

We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…

Mathematical Physics · Physics 2019-07-24 Steven Gassner , Carlo Cafaro

In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…

Quantum Physics · Physics 2018-04-04 N. Metwally

The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using…