Related papers: Information geometry of Euclidean quantum fields
The theory of $F$-manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We consider the quantum information metric of a family of CFTs perturbed by an exactly marginal operator, which has the dual description of the Euclidean Janus geometries. We first clarify its two dimensional case dual to the three…
We establish a previously unexplored conservation law for the Quantum Fisher Information Matrix (QFIM) expressed as follows; when the QFIM is constructed from a set of observables closed under commutation, i.e., a Lie algebra, the spectrum…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes…
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…
More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically…
We study quasi-Newton methods from the viewpoint of information geometry induced associated with Bregman divergences. Fletcher has studied a variational problem which derives the approximate Hessian update formula of the quasi-Newton…
Information geometry promotes an investigation of the geometric structure of statistical manifolds, providing a series of elucidations in various areas of scientific knowledge. In the physical sciences, especially in quantum theory, this…
Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier" due to the fact that the Fisher-Rao metric is now a functional incurring difficulties in defining its inverse. This paper introduces…
The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…
We argue that a consistent coupling of a quantum theory to gravity requires an extension of ordinary `first order' Riemannian geometry to second order Riemannian geometry, which incorporates both a line element and an area element. This…
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory. This theory describes the geometric features of the statistical manifold $\mathcal{M}$ of random events that are described by a…
We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
The search for a mathematical foundation for the path integral of Euclidean quantum gravity calls for the construction of random geometry on the spacetime manifold. Following developments in physics on the two-dimensional theory, random…
This article is devoted to some interesting geometric and informatic interpretations of peculiarities of 2D quantum field theory, which become re- vealed after its visualization. Contents. I. Geometry of Mobilevision: 1.1. Interpretational…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…