Rate degradation in quantum repeaters with imperfect memories

Memory dephasing and its impact on the rate of entanglement generation in quantum repeaters is addressed. For systems that rely on probabilistic schemes for entanglement distribution and connection, we estimate the maximum achievable rate per employed memory for our optimized partial nesting protocol. We show that, the polynomial scaling of rate with distance, L, can only be achieved if quantum memories with infinitely long coherence times are available. For finite coherence times and for long distances, the above rate degrades exponentially in root L regardless of the employed purification protocol.