According to the relevant theories on duality relation, the summation of the extractable information of a quanton's wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation.

中文翻译：

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波粒二象性关系与量子路径检测器

根据对偶关系的相关理论，分别以干涉可见度 V 和路径可区分性 D 为特征的量子波和粒子属性的可提取信息的总和是有限的。然而，这种关系在由量子分束器 (QBS) 引起的量子波态和粒子态之间的量子叠加时被破坏。另一方面，最近的研究已经将 l1 范数测量中的量子相干 C 作为波动特性的候选者。在这项研究中，我们提出了一种带有量子路径检测器（QWPD）的干涉仪，并检查了基于 C 的广义对偶关系。我们发现这种关系在这种情况下仍然成立，但是当 QWPD 系统部分存在时，这两种特性之间的干扰会导致观察到全粒子特性。使用一对偏振纠缠光子，我们通过实验验证了我们在双路径情况下的分析。本研究将相干性和路径信息之间的对偶关系扩展到量子情况，揭示了量子叠加对二元关系的影响。