Memory imperfections in atomic-ensemble-based quantum repeaters

Quantum repeaters promise to deliver long-distance entanglement overcoming loss in realistic quantum channels. A promising class of repeaters, based on atomic ensemble quantum memories and linear optics, follows the proposal by L.-M. Duan , Nature (London) 414, 413 (2001). Here we analyze 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 we 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 proposal of Duan, Lukin, Cirac, and Zoller.