Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras

• URL: http://arxiv.org/abs/2010.14394v2
• Date: Mon, 30 Nov 2020 09:46:24 GMT
• Title: Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras
• Authors: Florio M. Ciaglia, J\"urgen Jost, Lorenz Schwachh\"ofer
• Abstract summary: A geometrical formulation of estimation theory for finite-dimensional $Cstar$-algebras is presented. The derivation of the Cramer-Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A geometrical formulation of estimation theory for finite-dimensional $C^{\star}$-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer-Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.

Related papers

• Quantum geometry in many-body systems with precursors of criticality [0.0]
  We analyze the geometry of the ground-state manifold in parameter-dependent many-body systems with quantum phase transitions (QPTs) We elucidate the role of diabolic points in the formation of first-order QPTs, showing that these isolated geometric singularities represent seeds generating irregular behavior of geodesics in finite systems.
  arXiv  Detail & Related papers  (2024-11-06T15:06:05Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Intrinsic Bayesian Cramér-Rao Bound with an Application to Covariance Matrix Estimation [49.67011673289242]
  This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a smooth manifold. It induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure.
  arXiv  Detail & Related papers  (2023-11-08T15:17:13Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Monotone metric tensors in Quantum Information Geometry [0.0]
  We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem.
  arXiv  Detail & Related papers  (2022-03-21T10:28:02Z)
• A Unifying and Canonical Description of Measure-Preserving Diffusions [60.59592461429012]
  A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework. We develop a geometric theory that improves and generalises this construction to any manifold.
  arXiv  Detail & Related papers  (2021-05-06T17:36:55Z)
• Stochastic Quantization of Relativistic Theories [0.0]
  It was shown recently that quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian using second order differential geometry. We show that restrictions to relativistic theories can be obtained from this theory by imposing a energy-momentum relation.
  arXiv  Detail & Related papers  (2021-03-03T16:11:58Z)
• Geometric and algebraic approaches to quantum theory [0.0]
  We show how to formulate physical theory taking as a starting point the set of states. The equations of motion and the formulas for probabilities of physical quantities are analyzed.
  arXiv  Detail & Related papers  (2021-02-18T06:39:01Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)
• Geometric Formulation for Discrete Points and its Applications [0.0]
  We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions.
  arXiv  Detail & Related papers  (2020-02-07T01:12:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.