Entanglement Sudden Death as an Indicator of Fidelity in a Four-Qubit Cluster State

TL;DR

This paper investigates how entanglement sudden death in a four-qubit cluster state under dephasing affects its usefulness for quantum computation, finding that ESD signals when fidelity drops to 0.5 but does not cause fidelity discontinuities.

Contribution

It demonstrates that entanglement sudden death can serve as an indicator of fidelity decline in a four-qubit cluster state during quantum operations.

Findings

ESD does not cause fidelity discontinuities.

ESD indicates when fidelity drops to 0.5.

Fidelity remains continuous despite ESD.

Abstract

I explore the entanglement evolution of a four qubit cluster state in a dephasing environment concentrating on the phenomenon of entanglement sudden death (ESD). Specifically, I ask whether the onset of ESD has an effect on the utilization of this cluster state as a means of implementing a single qubit rotation in the measurement based cluster state model of quantum computation. To do this I compare the evolution of the entanglement to the fidelity, a measure of how accurately the desired state (after the measurement based operations) is achieved. I find that ESD does not cause a change of behavior or discontinuity in the fidelity but may indicate when the fidelity of certain states goes to .5.