Measurements and Information in Spin Foam Models

TL;DR

This paper explores the relationship between measurements and information theory within spin foam models of quantum gravity, focusing on Shannon entropy calculations for spin network graphs in three dimensions.

Contribution

It introduces a general framework for analyzing information in spin foam models and computes Shannon entropy for specific examples, revealing new inequalities.

Findings

Computed Shannon entropy for various spin network graphs

Identified interesting inequalities related to entropy in spin foam models

Provided a general definition linking measurements and information in quantum gravity

Abstract

We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy associated to the corresponding information. We present a general definition, compute the Shannon entropy of some examples, and find some interesting inequalities.