Wave-particle duality relations are fundamental for quantum physics. Previous experimental studies of duality relations mainly focus on the quadratic relation D² + V² ≤ 1, based on symmetric beam interference, while a linear form of the duality relation, predicated earlier theoretically, has never been experimentally tested. In addition, the difference between the quadratic form and the linear form has not been explored yet. In this work, with a designed asymmetric beam interference and by utilizing the polarization degree of freedom of the photon as a which-way detector, we experimentally confirm both forms of the duality relations. The results show that more path information is obtained in the quadratic case. Our findings reveal the difference between the two duality relations and have fundamental implications in better understanding these important duality relations.

波粒二象性关系是量子物理学的基础。以往对偶关系的实验研究主要集中在二次关系D ²  +  V ² ≤ 1，基于对称光束干涉，而对偶关系的线性形式，早先在理论上预测，从未经过实验测试。此外，尚未探索二次形式和线性形式之间的差异。在这项工作中，通过设计的不对称光束干涉和利用光子的偏振自由度作为双向检测器，我们通过实验确认了对偶关系的两种形式。结果表明，在二次情况下获得了更多的路径信息。我们的研究结果揭示了两种二元关系之间的差异，并对更好地理解这些重要的二元关系具有根本意义。