Bounding relative entropy for non-unitary excitations in quantum field theory

TL;DR

This paper develops a method to bound the relative entropy between quantum states in quantum field theory using convexity of non-commutative L^p norms, applicable to complex algebra types.

Contribution

It introduces a general bounding technique for relative entropy in von Neumann algebras without needing the relative modular operator, applicable to type III algebras in QFT.

Findings

Bounded the relative entropy for the chiral current on a light ray.

Applicable to local algebras of type III in quantum field theory.

Provided bounds for a dense set of single-particle states.

Abstract

We show how one can use the convexity of non-commutative $L^p$ norms to bound the relative entropy between a faithful state on a von Neumann algebra and an arbitrary excitation thereof. Our results hold for general von Neumann algebras, including the local algebras of type III that are ubiquitous in quantum field theory, and do not require knowledge of the relative modular operator. As an application of our results, we prove that for the chiral current on a light ray, the relative entropy between the vacuum and a dense set of single-particle states is uniformly bounded.