Qubit-environment Negativity versus Fidelity of conditional environmental states for an NV-center spin qubit interacting with a nuclear environment

TL;DR

This paper investigates the relationship between qubit-environment entanglement and the fidelity of environmental states in NV-center spin qubits, revealing their proportionality during decoherence processes.

Contribution

It demonstrates that Negativity and environmental state fidelity are closely related, providing a new way to distinguish entangling from non-entangling decoherence in NV-center systems.

Findings

Negativity and fidelity evolution show remarkable agreement.

Entanglement is proportional to the environmental trace.

Results apply across a wide range of parameters.

Abstract

We study the evolution of qubit-environment entanglement, quantified using Negativity, for NV-center spin qubits interacting with an environment of $^{13}$C isotope partially polarized nuclear spins in the diamond lattice. We compare it with the evolution of the Fidelity of environmental states conditional on the pointer states of the qubit, which can serve as a tool to distinguish between entangling and non-entangling decoherence in pure-dephasing scenarios. The two quantities show remarkable agreement during the evolution in a wide range of system parameters, leading to the conclusion that the amount of entanglement generated between the qubit and the environment is proportional to the trace that the joint evolution leaves in the environment.