Related papers: Towards quantifying information flows: relative en…
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 study the low-energy physics of the critical (2+1)-dimensional random transverse-field Ising model. The one-dimensional version of the model is a paradigmatic example of a system governed by an infinite-randomness fixed point, for which…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the…
At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…
We study holographic c-theorems based on timelike entanglement entropy and show that a timelike c-function captures irreversible renormalization group (RG) flow. We demonstrate that timelike c-functions are applicable to both relativistic…
We have applied our recent approach (Kargarian, et.al Phys. Rev. A 76, 60304 (R) (2007)) to study the quantum information properties of the anisotropic s=1/2 Heisenberg chain. We have investigated the underlying quantum information…
A central physical question is the extent to which infrared (IR) observations are sufficient to reconstruct a candidate ultraviolet (UV) completion. We recast this question as a problem of communication, with messages encoded in field…
The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and…
Information theoretic quantities play a central role in machine learning. The recent surge in the complexity of data and models has increased the demand for accurate estimation of these quantities. However, as the dimension grows the…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field…
We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant…
We explore the connection between deep learning and information theory through the paradigm of diffusion models. A diffusion model converts noise into structured data by reinstating, imperfectly, information that is erased when data was…
The notion of information scrambling is tied to the long-time behaviour of a system and therefore is related to its infra-red dynamics. In fast scramblers, information spreads as a logarithmic function of the number of degrees of freedom.…
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit \beta/a<<1 of a massive field theory in 3-dimensional spherical spaces M_3 with constant curvature 6/a^2. For…
In this paper we continue the study of renormalized entanglement entropy introduced in [1]. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…