连续发射源的贝尔不等式
Bell Inequalities for Continuously Emitting Sources
摘要：
证明非经典关联的一个常见实验策略是通过测量连续发射的纠缠光子对流来证明贝尔不等式的违反。测量涉及由两个空间上分离的方检测光子。记录并比较检测时间以量化违规。违规关键取决于确定哪些检测是重合的。由于记录的检测时间具有“抖动”，因此无法完美地推断出巧合。在存在依赖于设置的定时误差的情况下，这可以允许局部现实系统显示明显的违规-所谓的“巧合漏洞”。在这里，我们介绍了一个家庭的贝尔不等式的基础上签署，有向距离双方的序列记录的标记。考虑到在同步、固定的观测周期内记录的时间标记，以及设置选择是随机的且与源无关，违反这些不等式明确地显示了违反局部现实的非经典相关性。基于距离的贝尔不等式通常适用于测量结果空间的有效大小很大或无限大的两方配置。我们展示了如何系统地修改底层贝尔函数，以提高信噪比和量化的违反的意义。
英文摘要：
A common experimental strategy for demonstrating non-classical correlations is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. The measurements involve the detection of photons by two spatially separated parties. The detection times are recorded and compared to quantify the violation. The violation critically depends on determining which detections are coincident. Because the recorded detection times have "jitter", coincidences cannot be inferred perfectly. In the presence of settings-dependent timing errors, this can allow a local-realistic system to show apparent violation--the so-called "coincidence loophole". Here we introduce a family of Bell inequalities based on signed, directed distances between the parties' sequences of recorded timetags. Given that the timetags are recorded for synchronized, fixed observation periods and that the settings choices are random and independent of the source, violation of these inequalities unambiguously shows non-classical correlations violating local realism. Distance-based Bell inequalities are generally useful for two-party configurations where the effective size of the measurement outcome space is large or infinite. We show how to systematically modify the underlying Bell functions to improve the signal to noise ratio and to quantify the significance of the violation.
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