Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.

控制光子量子态的演化对于大多数量子信息处理和计量任务至关重要。由于其重要性，许多量子态演化机制已经过详细测试并得到了很好的理解；然而，演化波的基本相位异常，称为 Gouy 相位，在光的基本量子态的背景下进行的研究数量有限，特别是在光子数态的情况下。在这里，我们概述了一种计算传播时量子态演化的简单方法，并通过实验证明了这种量子 Gouy 相如何影响双光子量子态。我们的结果表明，多光子状态的相位敏感性增加也延伸到了这种基本的相位异常，并且必须考虑到以充分理解状态演化。