发表机构
Manning College of Information and Computer Sciences University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校曼宁信息与计算机科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对量子网络中路径选择与配置的联合优化问题，提出基于分层图的最短路径方法，单次运行获得速率-保真度帕累托前沿，支持任意非递减效用函数，并证明其近似最优性与可靠性。
AI 中文摘要
量子网络中的路径是连接两个用户并分发纠缠的中继器链。选择路径需要权衡所分发纠缠的速率和质量（例如保真度），但这些量不同于标准路由度量，它们是非加性组合的。链路级配置选择（例如蒸馏轮次或发射器亮度调节）进一步加剧了该问题，每种配置都在速率和保真度之间进行权衡，因此路径的性能取决于其路由和逐链路设置的联合作用。我们将这一联合路径选择与配置问题建模为分层图上的最短路径计算，其中分层图的层跟踪离散化的端到端保真度。单次运行即可返回完整的速率-保真度帕累托前沿，从中可以选择最大化速率和保真度的任何非递减效用函数的路径。我们证明，对于某些效用函数（包括BB84的密钥率），该方法是一个完全多项式时间近似方案，在指定容差内返回近最优路径。我们进一步精确刻画了何时更简单的基于标量化的路由就足够：对于具有凸保真度分布的效用函数，它是最优的，但在其他情况下（例如阶梯状、S形效用函数）可能任意次优，而分层方法在所有情况下都保持可靠。
英文摘要
A path in a quantum network is a chain of repeaters that distributes entanglement between two users. Selecting a path requires balancing the rate and quality (e.g., fidelity) of the delivered entanglement, but these quantities, unlike standard routing metrics, compose non-additively. The problem is compounded by link-level configuration choices (e.g., distillation rounds or emitter brightness tuning), each trading rate against fidelity, so that a path's performance depends jointly on its route and its per-link settings. We cast this joint path selection and configuration problem as a shortest path computation on a layered graph whose layers track discretized end-to-end fidelity. A single run returns the full rate fidelity Pareto frontier, from which the path maximizing any nondecreasing utility function of rate and fidelity can be selected. We prove that for certain utility functions (including the secret key rate of BB84), the method is a fully polynomial time approximation scheme, returning a near-optimal path within a specified tolerance. We further characterize exactly when cheaper scalarization-based routing suffices: it is optimal for utility functions with convex fidelity profiles, but can be arbitrarily suboptimal otherwise (e.g., for step-like, sigmoidal utilities), whereas the layered method remains reliable in all cases.
Comments13 pages
