AI 中文总结
该研究针对路径纠缠数态的Bell不等式违背问题，给出含多因素的闭合关联函数，指出无需光子数分辨的奇偶性探测更稳健，当前总效率下需0.92模式重叠，且重叠与预报效率存在权衡。
AI 中文摘要
一个在两个模式上离域的单光子是纠缠的，该纠缠能否违背Bell不等式的问题已争论了三十年。原则上该问题已解决：剩余的异议是缺乏共享相位参考，而本地振荡器可提供该参考，其作为共享框架而非测量设置发挥作用。实际上该问题仍未解决，剩余疑问在于装置本身。损耗对奇偶性测量的破坏远小于对其的缩放，使其落入已包含开关探测的同一单参数探测器算子族中。在该族内，我们给出了路径纠缠数态（即N00N态）在任意效率、暗计数、模式失配、相位噪声及上游损耗下的闭合关联函数。由于损耗与位移在位移振幅缩放意义上可对易，位移前后的损耗可互换，对称实验由一个总效率决定：即预报光子被探测到的概率。对于单光子，开关探测下的Clauser–Horne–Shimony–Holt效率阈值为0.83，奇偶性探测下为0.95，因此无需光子数分辨的方案更稳健，可容忍12个百分点的损耗及5倍的暗计数。效率不再是障碍，模式重叠才是。已演示的最佳电信耦合、可构建的干涉仪及当前探测器给出的总效率为0.86，此时所需重叠为0.92。我们表明该重叠同时包含预报光子的单模权重及本地振荡器的模式匹配，因此获取更多重叠会降低预报效率——尚无光源同时报道这两个参数。
英文摘要
A single photon delocalised over two modes is entangled, and whether that entanglement can violate a Bell inequality has been disputed for three decades. In principle it is settled: the surviving objection was the absence of a shared phase reference, and a local oscillator supplies one, acting as a shared frame rather than as a measurement setting. In practice it is open, and what remains is a question about the apparatus. Loss does not spoil a parity measurement so much as rescale it, carrying it into the same one-parameter family of detector operators that already contains on--off detection. Within that family we give closed correlators for path-entangled number states, or N00N states, at arbitrary efficiency, with dark counts, mode mismatch, phase noise and upstream loss. Because loss and displacement commute up to a rescaling of the displacement amplitude, loss before and after the displacement is interchangeable, and a symmetric experiment is governed by one overall efficiency: the probability that a heralded photon is detected. For a single photon the Clauser--Horne--Shimony--Holt threshold on that efficiency is 0.83 with on--off detection and 0.95 with parity, so the scheme that needs no photon-number resolution is the more robust, by twelve percentage points of loss and a factor of five in tolerable dark counts. Efficiency is no longer the obstacle; the mode overlap is. The best demonstrated telecom coupling, a buildable interferometer and today's detectors give an overall efficiency of 0.86, at which the required overlap is 0.92. We show that this overlap carries the heralded photon's single-mode weight as well as the local oscillator's mode match, so buying more of it costs heralding efficiency --- and no source has reported the two together.
Comments16 pages, 3 figures, 2 tables
