A quantum communication architecture is being developed for long-distance, high-fidelity qubitteleportation. It uses an ultrabright narrowband source of polarization-entangled photons, plus trapped-atom quantum memories, and it is compatible with long-distance transmission over standard telecommunication fiber. This paper reports error models for the preceding teleportationarchitecture, and for an extension thereto which enables long-distance transmission and storage of Greenberger-Horne-Zeilinger states. The use of quantum error correction or entanglement purification
to improve the performance of these quantum communication architectures is also discussed.