Kerr‐Effect‐Based High‐Dimensional Entanglement Generation for Qudit Systems

Abstract Employing high‐dimensional photonic encodings (qudits) instead of the traditional 2D encodings (qubits) can significantly enhance loss tolerance and reduce computational resources in photon‐based quantum information technology (QIT). To tap into this potential, effective schemes for the high‐dimensional generation of entangled states are essential. In this study, two arbitrary 4D entanglement generation protocols based on cross‐Kerr effect are developed, including two‐qudit entangled states with two photon pairs and three‐qudit entangled states with three photon pairs. These 4D entangled states require neither auxiliary photons (or entangled states) nor complicated quantum circuits. The success probabilities of high‐dimensional entangled states are close to 1 and their fidelities are robust against the photon loss with the current technology. The 4D entangled states depend on only simple linear‐optics elements, available four‐dimensional single‐qudit operations, and mature measurement methods, making our proposed protocols feasible and efficient in practical QIT.