# Entanglement generation between a charge qubit and its bosonic environment during pure dephasing - dependence on environment size

## TL;DR

This paper investigates how the size and initial mixedness of a bosonic environment influence the entanglement generated with a charge qubit during pure dephasing, revealing that entanglement diminishes with larger, more mixed environments.

## Contribution

It analytically demonstrates the dependence of environment size and initial mixedness on entanglement generation during pure dephasing of a charge qubit.

## Key findings

- Entanglement is independent of environment size for a pure initial state.
- Entanglement decreases as environment size increases for mixed initial states.
- No entanglement is generated at finite temperature in infinitely large environments.

## Abstract

We study entanglement generated between a charge qubit and a bosonic bath due to their joint evolution which leads to pure dephasing of the qubit. We tune the parameters of the interaction, so that the decoherence is quantitatively independent of the number of bosonic modes taken into account and investigate, how the entanglement generated depends on the size of the environment. A second parameter of interest is the mixedness of the initial state of the environment which is controlled by temperature. We show analytically that for a pure initial state of the environment, entanglement does not depend on environment size. For mixed initial states of the environment, the generated entanglement decreases with the increase of environment size. This effect is stronger for larger temperatures, when the environment is initially more mixed, but in the limit of an infinitely large environment, no entanglement is created at any finite temperature.