Quantum repeaters with imperfect memories: Cost and scalability

TLDR

Memory dephasing limits entanglement generation rates in quantum repeaters. With probabilistic entanglement schemes, the optimized partial nesting protocol yields a maximum rate per memory that scales polynomially with distance for ideal or fault‑tolerant memories, but falls to an exponential‑in‑√L (or at best exponential‑in‑L without purification) when memories have finite coherence and no fault‑tolerance.

Abstract

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, when a large number of memories are being used in each node. The above rate scales polynomially with distance, $L$, if quantum memories with infinitely long coherence times are available or if we employ a fully fault-tolerant scheme. For memories with finite coherence times and no fault-tolerant protection, the above rate optimistically degrades exponentially in $\sqrt{L}$, regardless of the employed purification scheme. It decays, at best, exponentially in $L$ if no purification is used.