Noncommutative metasurfaces enabled diverse quantum path entanglement of structured photons

Quantum entanglement, a fundamental concept in quantum mechanics, lies at the heart of many current and future quantum technologies. A pivotal task is generation and control of diverse quantum entangled states in a more compact and flexible manner. Here, we introduce an approach to achieve diverse path entanglement by exploiting the interaction between noncommutative metasurfaces and entangled photons. Different from other path entanglement, our quantum path entanglement is evolvement path entanglement of photons on Poincar\'e sphere. Due to quantum entanglement between idler photons and structured signal photons, evolvement path of idler photons on the fundamental Poincar\'e sphere can be nonlocally mirrored by structured signal photons on any high-order Poincar\'e sphere, resulting in quantum path entanglement. Benefiting from noncommutative metasurfaces, diverse quantum path entanglement can be switched across different higher-order Poincar\'e spheres using distinct combination sequences of metasurfaces. Our method allows for the tuning of diverse quantum path entanglement across a broad spectrum of quantum states, offering a significant advancement in the manipulation of quantum entanglement.