  We investigate the influence of noise on a graph state generation scheme
which exploits a mirror inverting spin chain. Within this scheme the spin chain
is used repeatedly as an entanglement bus (EB) to create multi-partite
entanglement. The noise model we consider comprises of each spin of this EB
being exposed to independent local noise which degrades the capabilities of the
EB. Here we concentrate on quantifying its performance as a single-qubit
channel and as a mediator of a two-qubit entangling gate, since these are basic
operations necessary for graph state generation using the EB. In particular,
for the single-qubit case we numerically calculate the average channel fidelity
and whether the channel becomes entanglement breaking, i.e., expunges any
entanglement the transferred qubit may have with other external qubits. We find
that neither local decay nor dephasing noise cause entanglement breaking. This
is in contrast to local thermal and depolarizing noise where we determine a
critical length and critical noise coupling, respectively, at which
entanglement breaking occurs. The critical noise coupling for local
depolarizing noise is found to exhibit a power-law dependence on the chain
length. For two qubits we similarly compute the average gate fidelity and
whether the ability for this gate to create entanglement is maintained. The
concatenation of these noisy gates for the construction of a five qubit linear
cluster state and a Greenberger-Horne-Zeilinger state indicates that the level
of noise that can be tolerated for graph state generation is tightly
constrained.
