Related papers: On Information Theory, Spectral Geometry and Quant…
Requiring black hole evaporation to be quantum-mechanically coherent imposes a universal, finite ``holographic bound'', conjectured to be due to fundamental discreteness of quantized gravity, on the amount of information carried by any…
Describing and understanding the essence of quantum entanglement and its connection to dynamical chaos is of great scientific interest. In this work, using information geometric (IG) techniques, we investigate the effects of…
We consider the entanglement entropy for a spacetime region and its spacelike complement in the framework of algebraic quantum field theory. For a M\"obius covariant local net satisfying a certain nuclearity property, we consider the von…
Optimization in large language models (LLMs) unfolds over high-dimensional parameter spaces with non-Euclidean structure. Information geometry frames this landscape using the Fisher information metric, enabling more principled learning via…
We discuss new approach to mathematical foundations of quantum theory, which is completely independent of Hilbert spaces and measure spaces. New kinematics is defined by non-linear geometry of spaces of integrals on abstract non-commutative…
In the cosmological context an effective quantum field theory describing the behavior of visible matter in the universe is characterized with its inherent UV cutoff and also with an IR scale that is set by the cosmological (particle)…
A coarse-graining of spin networks is expressed in terms of partial tracing, thus allowing to use tools of quantum information theory. This is illustrated by the analysis of a simple black hole model, where the logarithmic correction of the…
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth…
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any effective smooth field theoretical description would miss part of the fundamental degrees of freedom…
In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups,…
The possibility to describe the laws of the Universe in a computational way seems to be correlated to a principle that the density of information is bounded. This principle, that is dual to that of a finite velocity of information, has…
We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…
A longstanding question in quantum gravity regards the localization of quantum information; one way to formulate this question is to ask how subsystems can be defined in quantum-gravitational systems. The gauge symmetry and necessity of…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
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…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which do not have…
I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic…