Memory Imperfections in Atomic Ensemble-based Quantum Repeaters

Quantum repeaters promise to deliver long-distance entanglement overcoming noise and loss in realistic quantum channels. A promising class of repeaters, based on atomic ensemble quantum memories and linear optics, follow the proposal by Duan et al [Nature 414, 413, 2001]. Here we analyse this protocol in terms of a very general model for the quantum memories employed. We derive analytical expressions for scaling of entanglement with memory imperfections, dark counts, loss and distance, and apply our results to two specific quantum memory protocols. Our methods apply to any quantum memory with an interaction Hamiltonian at most quadratic in the mode operators and are in principle extendible to more recent modifications of the original DLCZ proposal.