Geometry of the Shannon mutual information in continuum QFT

Abstract

We analyze geometric terms and scaling properties of the Shannon mutual information in the continuum. This is done for a free massless scalar field theory in $d$-dimensions, in a coherent state reduced with respect to a general differentiable manifold. As a by-product, we find an expression for the reduced probability density of finding a certain field on a ball. We will also introduce and compute the Fisher information that this probability carries about the location of the observation region. This is an interesting information measure that refers to points in physical space, although in relativistic QFT they are labels and not fluctuating quantum observables.

25 pages

References in corpus (1)

• Renyi Entropy and Geometry

Cited by in corpus (3)

• Information geometry in quantum field theory: lessons from simple examples
• Multipartite entanglement and quantum Fisher information in conformal field theories
• Geometric Rényi mutual information induced by localized particle excitations in quantum field theory