The wave–particle duality relation derived by Englert sets an upper bound of the extractable information from wave and particle properties in a two-path interferometer. Surprisingly, previous studies demonstrated that the introduction of a quantum beamsplitter in the interferometer could break the limitation of this upper bound, due to interference between wave and particle states. Along the other line, a lot of efforts have been made to generalize this relation from the two-path setup to the N-path case. Thus, it is an interesting question that whether a quantum N-path beamsplitter can break the limitation as well. This paper systemically studies the model of a quantum N-path beamsplitter, and finds that the generalized wave–particle duality relation between interference visibility and path distinguishability is also broken in certain situations. We further study the maximal extractable information’s reliance on the interference between wave and particle properties, and derive a quantitative description. We then propose an experimental methodology to verify the break of the limitation. Our work reflects the effect of quantum superposition on wave–particle duality, and exhibits a new aspect of the relation between visibility and path distinguishability in N-path interference. Moreover, it implies the observer’s influence on wave–particle duality.

由 Englert 推导出的波粒二象性关系设定了双路径干涉仪中从波和粒子特性中可提取信息的上限。令人惊讶的是，先前的研究表明，由于波和粒子状态之间的干涉，在干涉仪中引入量子分束器可以打破这个上限的限制。另一方面，已经做出了很多努力来将这种关系从双路径设置推广到N路径情况。因此，一个有趣的问题是量子N路分束器是否也能打破这一限制。本文系统地研究了一个量子N的模型-路径分束器，并发现干涉可见性和路径可分辨性之间的广义波粒二象性关系在某些情况下也被打破。我们进一步研究了最大可提取信息对波粒干涉特性的依赖，并得出了定量描述。然后，我们提出了一种实验方法来验证限制的突破。我们的工作反映了量子叠加对波粒二象性的影响，并展示了N路径干涉中可见性和路径可分辨性之间关系的新方面。此外，它暗示了观察者对波粒二象性的影响。