标题： 频率分辨的高纠缠双光子态模拟：超越单对近似。 一. 理论 显示英文标题

标题： Frequency-Resolved Simulations of Highly Entangled Biphoton States: Beyond the Single-Pair Approximation. I. Theory

摘要： 我们讨论了双光子态检测概率在联合频谱振幅高阶展开中的扩展。 该展开使得涉及表现出高度频谱纠缠的量子态的高效时间或频率分辨数值模拟成为可能。 与基于单对或双对近似的常规方法不同，我们根据不同对之间的相关性数量来展开表达式。 最低的展开阶数对应于无限纠缠态的极限，在此情况下，不同的对完全不相关，且所有多对统计信息都从单对推断得出。 我们证明，即使在这种极限情况下，结果也总是比单对近似更准确。 更高的展开阶数描述了与无限纠缠情况的偏差，并在不同对的光子之间引入了相关性。 显示英文摘要

摘要： We discuss an expansion of the detection probabilities of biphoton states in terms of increasing orders of the joint spectral amplitude. The expansion enables efficient time- or frequency-resolved numerical simulations involving quantum states exhibiting a high degree of spectral entanglement. Contrary to usual approaches based on one- or two-pair approximations, we expand the expressions in terms corresponding to the amount of correlations between different pairs. The lowest expansion order corresponds to the limit of infinitely entangled states, where different pairs are completely uncorrelated and the full multi-pair statistics are inferred from a single pair. We show that even this limiting case always yields more accurate results than the single-pair approximation. Higher expansion orders describe deviations from the infinitely entangled case and introduce correlations between the photons of different pairs.