Single-photon entanglement, the entanglement between vacuum state and single-photon state, is essentially the entanglement of particle characteristics. Wave-particle duality indicates that wave property and particle property could coexist. Can we find evidence of wave-behavior entanglement in single-photon entanglement? Here, based on the construction of Bell-like inequality in wave space, we propose a method to verify the wave-particle duality in single-photon entanglement. First, we define the wave state in two-dimensional space relative to the photon number state, and propose a method to measure the wave state. The strong violation of Bell’s inequality based on the joint measurement of wave states indicates the existence of single-photon entanglement, and the wave is the conjugate variable of the particle. Wave state entanglement obtained from Fourier transform of single photon entanglement and the corresponding measurement protocols will provide us with more information-carrying schemes in the field of quantum information. The difference in the representation in photon-number space and wave space implies the wave-particle duality of single photon entanglement.

单光子纠缠，真空态和单光子态之间的纠缠，本质上是粒子特性的纠缠。波粒二象性表明波特性和粒子特性可以共存。我们能在单光子纠缠中找到波行为纠缠的证据吗？在这里，基于波空间中类贝尔不等式的构造，我们提出了一种验证单光子纠缠中波粒二象性的方法。首先，我们定义了二维空间中相对于光子数态的波态，并提出了一种测量波态的方法。基于波态联合测量的贝尔不等式的强烈违反表明单光子纠缠的存在，波是粒子的共轭变量。单光子纠缠傅里叶变换得到的波态纠缠以及相应的测量协议将为我们提供更多的量子信息承载方案。光子数空间和波空间表示的差异暗示了单光子纠缠的波粒二象性。