  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.
