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arXiv:2511.02337 · Journal of Physics B Atomic Molecular and Optical Physics

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

Jiping Wang, Huapeng Liu

quant-phSubmitted Nov 4, 2025• Announced Nov 5, 2025• 0 citations
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Abstract

Three-dimensional Bell states and GHZ states serve as representative examples of high-dimensional 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, dephasing effects and random noise. Numerical simulations indicate that the proposed scheme can achieve high fidelity.

Journal reference
Jiping Wang and Huapeng Liu 2025 J. Phys. B: At. Mol. Opt. Phys. 58 215501
DOI
10.1088/1361-6455/ae1536
Comments
12 pages,10 figures Published in J. Phys. B: At. Mol. Opt. Phys. (IOP Publishing)

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Three-dimensional Bell states and GHZ states serve as representative examples of high-dimensional 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, dephasing effects and random noise. Numerical simulations indicate that the proposed scheme can achieve high fidelity.
Abstract We propose a scheme for generating the three-dimensional (3D) entanglement between two Rydberg atoms. Two laser fields are imposed to drive two transitions of each atom. The Rydberg antiblockade is induced through the suitable choice of the relation among parameters. We propose to offset Stark shifts by introducing detuning compensation so as to induce an effective resonant three-level system concluding two collective ground states and the double-excitation state, instead of introducing the complicated auxiliary levels and laser fields. Four 3D entangled states are calculated out, and numerical simulations show that the high-fidelity 3D entanglement can be generated. The effect of the spontaneous radiations of the Rydberg states on the generation of the 3D entanglement is analyzed. In addition, we show the numerical search algorithm so as to get optimized parameters for shortening operation time and thus decreasing the decoherence accumulation.
High-dimensional quantum entanglement characterizes the entanglement of quantum systems within a larger Hilbert space, introducing more intricate and complex correlations among the entangled particles' states. The high-dimensional Greenberger–Horne–Zeilinger (GHZ) state, symbolic of this type of entanglement, is of significant importance in various quantum information processing applications. This study proposes integrating a neutral atom platform with quantum reservoir engineering to generate a high-dimensional GHZ state deterministically. Leveraging the advantages of neutral atoms in a modified unconventional Rydberg pumping mechanism, combined with controlled dissipation, we achieve a three-dimensional GHZ state with a fidelity surpassing 99% through multiple pump and dissipation cycles. This innovative approach paves the way for experimentally feasible, deterministic preparation of high-dimensional GHZ states in Rydberg atom systems, thereby advancing the capabilities of quantum information processing.
We extend the recent result of a bipartite Bell singlet [A. W. Carr and M. Saffman, Phys. Rev. Lett. 111, 033607 (2013)] to a stationary three-dimensional entanglement between two-individual neutral Rydberg atoms. This proposal makes full use of the coherent dynamics provided by a Rydberg-mediated interaction and the dissipative factor originating from the spontaneous emission of a Rydberg state. The numerical simulation of the master equation reveals that both the target state negativity $\mathcal{N}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\ensuremath{\infty}})$ and fidelity $\mathcal{F}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\ensuremath{\infty}})$ can exceed 99.90%. Furthermore, a steady three-atom singlet state $|{S}_{3}\ensuremath{\rangle}$ is also achievable based on the same mechanism.
Abstract A scheme to prepare a 3D entangled state between a pair of Rydberg atoms via dissipative dynamics and electromagnetic induced transparency associated with the single‐atom dark state is proposed. The prepared entangled state is the dark state of the whole system. The scheme is also feasible regardless of initial purity or mixed state. Since the proposed scheme is based on the Rydberg block regime, the Rydberg–Rydberg interaction strength does not need to satisfy a certain relation with laser detuning, which is very different to the Rydberg‐antiblock‐based dissipative schemes. One group of Rydberg states and corresponding parameters to simulate the fidelity are used, which verify the feasibility of the scheme.
Abstract By using the Lyapunov control approach—an optimization algorithm, we propose a dissipative scheme for efficiently preparing the three-dimensional entangled state of two Rydberg atoms, which subject to Rydberg–Rydberg interactions at the antiblockade regime. The steady target state is the unique dark state of the two-atom system, and is achieved with high fidelity under the Rydberg pumping and the atomic spontaneous emission. The time required to settle into the high-fidelity steady state is greatly accelerated by the help of Lyapunov control, which takes effects while the system is initially prepared in the states containing coherence between the dark state and decoherence-sensitive bright states. The numerical results show that a fidelity of the steady three-dimensional entangled state above 0.99 can be achieved around 2.2 ms with the current experimental conditions. We study in detail the optimal control parameters and show the robustness of the scheme against random noises. The scheme may be generalized for preparation of more complicate multi-atom entangled states.
The multipartite GHZ states are useful resources for quantum information processing. Here we put forward a scalable way to adiabatically prepare the multipartite GHZ states in a chain of Rydberg atoms. Building on the ground-state blockade effect of Rydberg atoms and the stimulated Raman adiabatic passage (STIRAP), we suppress the adverse effect of the atomic spontaneous emission, and obtain a high fidelity of the multipartite GHZ states without requirements on the operational time. After investigating the feasibility of the proposal, we show a 3-qubit GHZ state can be generated in a wide range of relevant parameters and a fidelity above $98\%$98% is achievable with the current experimental technologies.