Characterization and measurement of qubit-environment entanglement generation during pure dephasing

TL;DR

This paper investigates the conditions under which a qubit becomes entangled with its environment during pure dephasing, providing criteria for entanglement generation and its detectability, with implications for quantum decoherence.

Contribution

It presents a necessary and sufficient condition for qubit-environment entanglement during pure dephasing, linking entanglement to environmental state changes and detection methods.

Findings

Entanglement occurs under specific initial environmental states and interaction properties.

Detection of entanglement is possible via the Peres-Horodecki criterion.

Environmental state change accompanies entanglement in many cases.

Abstract

We consider the coupling of a qubit in a pure state to an environment in an arbitrary state, and characterize the possibility of qubit-environment entanglement generation during the evolution of the joint system, that leads to pure dephasing of the qubit. We give a simple necessary and sufficient condition on the initial density matrix of the environment together with the properties of the interaction, for appearance of qubit-environment entanglement. Any entanglement created turns out to be detectable by the Peres-Horodecki criterion. Furthermore, we show that for a large family of initial environmental states, the appearance of nonzero entanglement with the environment is necessarily accompanied by a change in the state of the environment (i.e. by the back-action of the qubit).