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

Jiping Wang, Huapeng Liu

TL;DR

This work addresses the challenge of generating high-dimensional entanglement, specifically 3D Bell and GHZ states, using Rydberg atoms. It constructs chain-like effective Hamiltonians $H_{eff}$ and $H_{fe}$ through detuning to simplify dynamics, and designs centrosymmetric Gaussian pulses with parameters $(A_k, \sigma_k, \theta_k)$ that are optimized via gradient-based methods and genetic algorithms. The approach demonstrates high fidelities under realistic decoherence modeled by a master equation and shows robustness to pulse noise, with concrete 87Rb implementations achieving near-ideal performance (e.g., Bell fidelity ~98% and GHZ fidelity ~97%). This method provides a scalable, single-evolution pathway to robust high-dimensional entanglement and offers a flexible framework for extending to other high-dimensional quantum states with Rydberg platforms.

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.

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

TL;DR

This work addresses the challenge of generating high-dimensional entanglement, specifically 3D Bell and GHZ states, using Rydberg atoms. It constructs chain-like effective Hamiltonians and through detuning to simplify dynamics, and designs centrosymmetric Gaussian pulses with parameters that are optimized via gradient-based methods and genetic algorithms. The approach demonstrates high fidelities under realistic decoherence modeled by a master equation and shows robustness to pulse noise, with concrete 87Rb implementations achieving near-ideal performance (e.g., Bell fidelity ~98% and GHZ fidelity ~97%). This method provides a scalable, single-evolution pathway to robust high-dimensional entanglement and offers a flexible framework for extending to other high-dimensional quantum states with Rydberg platforms.

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.

Paper Structure

This paper contains 6 sections, 21 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Physical Model and effective
  3. Three-dimensiona Bell state
  4. Three-dimensiona GHZ state
  5. Numerical simulations
  6. Summary

Figures (10)

  • Figure 1: Two Rydberg atoms with the interaction strength $V$.
  • Figure 2: Excitation scheme and relevant energy levels of atom $k$.
  • Figure 3: Three identical neutral atoms arranged in a triangular configuration.
  • Figure 4: Time evolution of the populations for the states $\ket{00}$, $\ket{11}$, $\ket{22}$.
  • Figure 5: The fidelity of the 3D Bell states versus the interaction time.
  • ...and 5 more figures