One-step preparation of 3D Bell and 3D GHZ states with Rydberg atoms

Three-dimensional Bell states and GHZ states serve as representative examples of highdimensional entangled states. In this paper, we propose a scheme for generating three-dimensional Bell and GHZ entangled states using Rydberg atoms. By leveraging Rydberg-mediated interactions and introducing detuning, the system is effectively simplified into a chain-like configuration. To design effective couplings, we employ a centrosymmetric Gaussian distribution and optimize the relevant parameters. Furthermore, we take into account decoherence factors including atomic spontaneous emission and dephasing effects. Numerical simulations indicate that the proposed scheme can achieve high fidelity.