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

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.