Superoperator Analysis of Entanglement in a Four-Qubit Cluster State

TL;DR

This paper uses superoperator formalism to analyze how entanglement in four-qubit cluster states evolves under decoherence, examining its impact on quantum computation fidelity and phenomena like entanglement sudden death.

Contribution

It introduces a superoperator-based method to study entanglement dynamics in four-qubit cluster states under decoherence, linking entanglement loss to computational fidelity.

Findings

Entanglement degrades under various decoherence models.

Entanglement sudden death can occur, affecting quantum computation.

Fidelity of logical qubit rotations correlates with entanglement levels.

Abstract

In this paper we utilize superoperator formalism to explore the entanglement evolution of four-qubit cluster states in a number of decohering environments. A four-qubit cluster state is a resource for the performance of an arbitrary single logical qubit rotation via measurement based cluster state quantum computation. We are specifically interested in the relationship between entanglement evolution and the fidelity with which the arbitrary single logical qubit rotation can be implemented in the presence of decoherence as this will have important experimental ramifications. We also note the exhibition of entanglement sudden death (ESD) and ask how severely its onset affects the utilization of the cluster state as a means of implementing an arbitrary single logical qubit rotation.