  We investigate different geometries of spin-1/2 nitrogen impurity channels
for distributing entanglement between pairs of remote nitrogen vacancy centers
(NVs) in diamond. To go beyond the system size limits imposed by directly
solving the master equation, we implement a matrix product operator method to
describe the open system dynamics. In so doing, we provide an early
demonstration of how this technique can be used for simulating real systems.
For a fixed NV separation there is an interplay between incoherent impurity
spin decay and coherent entanglement transfer: Long transfer time, few-spin
systems experience strong dephasing that can be overcome by increasing the
number of spins in the channel. We examine how missing spins and disorder in
the coupling strengths affect the dynamics, finding that in some regimes a spin
ladder is a more effective conduit for information than a single spin chain.

Quantum Physics;Mesoscale and Nanoscale Physics