At the core of the quantum Internet lie quantum repeaters that enable remote end-to-end entanglement generation. Fundamentally, the entanglement generation rate and fidelity of quantum repeaters constitute the bottleneck for end-to-end performance. To achieve high rates, quantum repeaters employ quantum memory multiplexing. In a high-rate standard repeater, each memory sequentially generates an entanglement with its neighboring nodes and then applies entanglement swapping. This, however, results in low fidelity due to decoherence of the first-formed entanglement in the sequential generation process. By allocating different numbers of memories to simultaneously form entanglements with the left and right adjacent nodes, quantum repeaters reduce high waiting times and achieve high fidelity. In such a repeater, a mismatch problem arises due to the difference between the probabilistic number of generated entanglements on both sides. Consequently, some entanglements remain stored until opposite entanglements are available. The mismatch problem reduces the repeater rate and particularly the entanglement fidelity. In this paper, we consider the mismatch problem in an asymmetric repeater with different distances to its adjacent nodes. To mitigate the mismatch problem, we derive a dynamic optimal memory allocation. Under the optimal allocation, we derive statistical lower bounds on the achievable rate and fidelity. We demonstrate that the optimal allocation significantly improves the fidelity while maintaining a comparable rate to the standard repeater. In contrast, our results show that fixed memory allocation may be detrimental to the fidelity.

翻译：量子互联网的核心在于量子中继器，它们能够实现远程端到端纠缠的生成。本质上，量子中继器的纠缠生成速率和保真度构成了端到端性能的瓶颈。为了达到高速率，量子中继器采用量子存储器复用技术。在高速率标准中继器中，每个存储器会依次与其相邻节点生成纠缠，然后执行纠缠交换。然而，由于顺序生成过程中最先形成的纠缠会发生退相干，这会导致保真度降低。通过分配不同数量的存储器，使其同时与左右相邻节点形成纠缠，量子中继器能够减少高等待时间并实现高保真度。在这种中继器中，由于两侧生成的纠缠数量存在概率性差异，会产生失配问题。因此，一些纠缠会一直存储，直到获得对侧的纠缠。失配问题会降低中继器的速率，特别是纠缠保真度。在本文中，我们考虑了一个到相邻节点距离不同的非对称中继器中的失配问题。为了缓解失配问题，我们推导出了一种动态最优存储器分配方案。在最优分配下，我们推导了可达速率和保真度的统计下界。我们证明，与标准中继器相比，最优分配在保持相当速率的同时，显著提高了保真度。相反，我们的结果表明，固定存储器分配可能对保真度有害。