# Infrared quantum information

## TL;DR

This paper explores how soft photons and gravitons cause decoherence in quantum states, computes their entanglement entropy, and shows it remains finite after resummation of divergences, advancing understanding of infrared quantum information.

## Contribution

It demonstrates the decoherence effects of soft bosons on outgoing states and calculates their entanglement entropy, revealing infrared finiteness through resummation techniques.

## Key findings

- Soft photons decohere nearly all outgoing charged particle states.
- Soft gravitons decohere nearly all outgoing states of all particles.
- Entanglement entropy of soft bosons is infrared-finite after resummation.

## Abstract

We discuss information-theoretic properties of low-energy photons and gravitons in the S-matrix. Given an incoming n-particle momentum eigenstate, we demonstrate that unobserved soft photons decohere nearly all outgoing momentum superpositions of charged particles, while the universality of gravity implies that soft gravitons decohere nearly all outgoing momentum superpositions of all the hard particles. Using this decoherence, we compute the entanglement entropy of the soft bosons and show that it is infrared-finite when the leading divergences are re-summed a la Bloch and Nordsieck.