# Production of Entanglement Entropy by Decoherence

## TL;DR

This paper rigorously analyzes how decoherence in a two-level system interacting with an oscillator environment leads to entanglement entropy production, identifying key oscillator frequencies involved.

## Contribution

It establishes a precise link between decoherence and entanglement entropy production, highlighting the specific environment oscillators responsible.

## Key findings

- Not all environment oscillators contribute equally to entanglement entropy.
- Identifies oscillator frequency regions that significantly produce entanglement entropy.
- Results are valid for arbitrary interaction strengths and are mathematically rigorous.

## Abstract

We examine the dynamics of entanglement entropy of all parts in an open system consisting of a two-level dimer interacting with an environment of oscillators. The dimer-environment interaction is almost energy conserving. We find the precise link between decoherence and production of entanglement entropy. We show that not all environment oscillators carry significant entanglement entropy and we identify the oscillator frequency regions which contribute to the production of entanglement entropy. Our results hold for arbitrary strengths of the dimer-environment interaction, and they are mathematically rigorous.