Universal conservation laws of the wave-particle-entanglement triad: theory and experiment

When observed, a quantum system exhibits either wave-like or particle-like properties, depending on how it is measured. However, this duality is affected by the entanglement of the system with its quantum memory, raising a fundamental question: how are wave–particle duality and entanglement related? Here, we broaden the scope of wave–particle duality to include entanglement, introduce universal conservation laws for the wave–particle–entanglement triad, and perform demonstrations on silicon–integrated nanophotonic quantum chips. Our experiments not only mark the first confirmation of universal conservation laws but also highlight the potential of integrated photonics for exploring complex quantum phenomena in high-dimensional systems.