Qubit-environment entanglement generation and the spin echo

TL;DR

This paper investigates how the spin echo protocol interacts with qubit-environment entanglement during pure dephasing, revealing that echo can reverse dephasing caused by both classical noise and entanglement, with entanglement sometimes generated after the echo pulse.

Contribution

It demonstrates that spin echo can undo entanglement-induced dephasing and identifies conditions where entanglement is generated post-echo, providing insights into entanglement detection via echo signals.

Findings

Echo can counteract entanglement-related dephasing.

Entanglement can be generated after the echo pulse at specific times.

Features of the echo signal can indicate entangling dynamics.

Abstract

We analyze the relationship between qubit-environment entanglement that can be created during the pure dephasing of the qubit and the effectiveness of the spin echo protocol. We focus here on mixed states of the environment. We show that while the echo protocol can obviously counteract classical environmental noise, it can also undo dephasing associated with qubit-environment entanglement, and there is no obvious difference in its efficiency in these two cases. Additionally, we show that qubit-environment entanglement can be generated at the end of the echo protocol even when it is absent at the time of application of the local operation on the qubit (the {\pi} pulse). We prove that this can occur only at isolated points in time, after fine-tuning of the echo protocol duration. Finally, we discuss the conditions under which the observation of specific features of the echo signal can serve as a witness of the entangling nature of the joint qubit-environment evolution.