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Quantum Engineering

Dissipative engineering of a tripartite Greenberger–Horne–Zeilinger state for neutral atoms

Dongxiao Li, Chong Yang, Xiao‐Qiang Shao

Published May 5, 2021• 7 citations
Publisher

Abstract

The multipartite Greenberger–Horne–Zeilinger (GHZ) states are indispensable elements for various quantum information processing tasks. Here we put forward two deterministic proposals to dissipatively prepare tripartite GHZ states in a neutral atom system. The first scheme utilizes the polychromatic driving fields and the engineered spontaneous emission of Rydberg states to generate a tripartite GHZ state with a high efficiency, which is then optimized by introducing the Gaussian soft control pulse. In the second scenario, we exploit the natural spontaneous emission of the Rydberg states as a resource, thence a steady tripartite GHZ state with fidelity around 98% can be obtained by simultaneously integrating the switching driving of unconventional Rydberg pumping and the Rydberg antiblockade effect.

DOI
10.1002/que2.66

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The multipartite Greenberger–Horne–Zeilinger (GHZ) states are indispensable elements for various quantum information processing tasks. Here we put forward two deterministic proposals to dissipatively prepare tripartite GHZ states in a neutral atom system. The first scheme utilizes the polychromatic driving fields and the engineered spontaneous emission of Rydberg states to generate a tripartite GHZ state with a high efficiency, which is then optimized by introducing the Gaussian soft control pulse. In the second scenario, we exploit the natural spontaneous emission of the Rydberg states as a resource, thence a steady tripartite GHZ state with fidelity around 98% can be obtained by simultaneously integrating the switching driving of unconventional Rydberg pumping and the Rydberg antiblockade effect.
The multipartite Greenberger-Horne-Zeilinger (GHZ) states are indispensable elements for various quantum information processing tasks. Here we put forward two deterministic proposals to dissipatively prepare tripartite GHZ states in a neutral atom system. The first scheme can be considered as an extension of a recent work [T. M. Wintermantel, Y. Wang, G. Lochead, \textit{et al}, {Phys. Rev. Lett. \textbf{124}, 070503 (2020)}]. By virtue of the polychromatic driving fields and the engineered spontaneous emission, a multipartite GHZ state with odd numbers of atoms are generated with a high efficiency. This scheme effectively overcomes the problem of dependence on the initial state but sensitive to the decay of Rydberg state. In the second scenario, we exploit the spontaneous emission of the Rydberg states as a resource, thence a steady tripartite GHZ state with fidelity around 98%98\%98% can be obtained by simultaneously integrating the switching driving of unconventional Rydberg pumping and the Rydberg antiblockade effect.
The multipartite Greenberger–Horne–Zeilinger (GHZ) states play an important role in large-scale quantum information processing. We utilize the polychromatic driving fields and the engineered spontaneous emissions of Rydberg states to dissipatively drive three- and four-partite neutral atom systems into the steady GHZ states, at the presence of the next-nearest neighbor interaction of excited Rydberg states. Furthermore, the introduction of quantum Lyapunov control can help us optimize the dissipative dynamics of the system so as to shorten the convergence time of the target state, improve the robustness against the spontaneous radiations of the excited Rydberg states, and release the limiting condition for the strengths of the polychromatic driving fields. Under the feasible experimental conditions, the fidelities of three- and four-partite GHZ states can be stabilized at 99.24 % and 98.76 %, respectively.
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.
Greenberger-Horne-Zeilinger and WWW states feature genuine tripartite entanglement that cannot be converted into each other by local operations and classical communication. Here, we present a dissipative protocol for deterministic interconversion between Greenberger-Horne-Zeilinger and WWW states of three neutral 87Rb{}^{87}\mathrm{Rb}87Rb atoms arranged in an equilateral triangle of a two-dimensional array. With three atomic levels and diagonal van der Waals interactions of Rydberg atoms, the interconversion between tripartite entangled states can be efficiently accomplished in the Floquet-Lindblad framework through the periodic optical pump and dissipation engineering. We evaluate the feasibility of the existing methodology using the experimental parameters accessible to current neutral-atom platforms. We find that our scheme is robust against typical noises, such as laser phase noise and geometric imperfections of the atom array. In addition, our scheme can integrate the Gaussian soft quantum control technique, which further reduces the overall conversion time and increases the resilience to timing errors and interatomic distance fluctuations. The high-fidelity and robust tripartite entanglement interconversion protocol provides a route to save physical resources and enhance the computational efficiency of quantum networks formed by neutral-atom arrays.
Inspired by a recent work [Reiter, Reeb, and Sorensen, Phys. Rev. Lett. {\bf117}, 040501 (2016)], we present a simplified proposal for dissipatively preparing a Greenberger-Horne-Zeilinger (GHZ) state of three Rydberg atoms in a cavity. The ZZZ pumping is implemented under the action of the spontaneous emission of Λ\LambdaΛ-type atoms and the quantum Zeno dynamics induced by strong continuous coupling. In the meantime, a dissipative Rydberg pumping breaks up the stability of the state ∣GHZ+⟩|{\rm GHZ}_+\rangle∣GHZ+​⟩ in the process of ZZZ pumping, making ∣GHZ−⟩|{\rm GHZ}_-\rangle∣GHZ−​⟩ be the unique steady state of system. Compared with the former scheme, the number of driving fields acting on atoms is greatly reduced and only a single-mode cavity is required. The numerical simulation of the full master equation reveals that a high fidelity ∼98%\sim98\%∼98% can be obtained with the currently achievable parameters in the Rydberg-atom-cavity system.
Inspired by a recent work [F. Reiter, D. Reeb, and A. S. S\o{}rensen, Phys. Rev. Lett. 117, 040501 (2016)], we present a simplified proposal for dissipatively preparing a Greenberger-Horne-Zeilinger (GHZ) state of three Rydberg atoms in a cavity. The ZZZ pumping is implemented under the action of the spontaneous emission of $\mathrm{\ensuremath{\Lambda}}$-type atoms and the quantum Zeno dynamics induced by strong continuous coupling. In the meantime, a dissipative Rydberg pumping breaks up the stability of the state $|{\mathrm{GHZ}}_{+}\ensuremath{\rangle}$ in the process of ZZZ pumping, making $|{\mathrm{GHZ}}_{\ensuremath{-}}\ensuremath{\rangle}$ the unique steady state of the system. Compared with the former scheme, the number of driving fields acting on atoms is greatly reduced and only a single-mode cavity is required. The numerical simulation of the full master equation reveals that a high fidelity $\ensuremath{\sim}98%$ can be obtained with the currently achievable parameters in the Rydberg-atom-cavity system.