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Communications in Theoretical Physics

Deterministic interconversion of the Greenberger–Horne–Zeilinger state and Knill–Laflamme–Milburn state via Lie-transform-based pulse design in Rydberg atoms

J. P. Wang, Yan‐Qiang Ji, L P Yang, C Q Wang, L Dong, Xiao‐Ming Xiu

Published Dec 16, 2024• 3 citations
Publisher

Abstract

Abstract Conversion between different types of entangled states is an interesting problem in quantum mechanics. But research on the conversion between the Greenberger–Horne–Zeilinger (GHZ) state and Knill–Laflamme–Milburn (KLM) state in an atomic system has not been reported. In this paper, we propose a scheme to realize the interconversion (one-step) between the GHZ state and KLM state with Rydberg atoms. By utilizing Rydberg-mediated interactions, we simplify the system. By combining a Lie-transform-based pulse design, the evolution path is built up to realize interconversion of the GHZ state and KLM state. The numerical simulation result shows that the present scheme is robust against decoherence and operational imperfection.

DOI
10.1088/1572-9494/ad9f48

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Abstract Conversion between different types of entangled states is an interesting problem in quantum mechanics. But research on the conversion between the Greenberger–Horne–Zeilinger (GHZ) state and Knill–Laflamme–Milburn (KLM) state in an atomic system has not been reported. In this paper, we propose a scheme to realize the interconversion (one-step) between the GHZ state and KLM state with Rydberg atoms. By utilizing Rydberg-mediated interactions, we simplify the system. By combining a Lie-transform-based pulse design, the evolution path is built up to realize interconversion of the GHZ state and KLM state. The numerical simulation result shows that the present scheme is robust against decoherence and operational imperfection.
Conversion between different types of entangled states is an interesting problem in quantum mechanics. But research on the conversion between Greenberger-Horne-Zeilinger (GHZ) state and Knill-Laflamme-Milburn (KLM) state in atomic system is absent. In this paper, we propose a scheme to realize the interconversion (one-step) between GHZ state and KLM state with Rydberg atoms. By utilizing Rydberg-mediated interactions, we simplify the system. By combining Lie-transform-based pulse design, the evolution path is built up to realize interconversion of GHZ state and KLM state. The numerical simulation result shows that the present scheme is robust against decoherence and operational imperfection, the analysis shows that the scheme is feasible with current experimental technology.
Abstract Schemes for converting photonic polarized‐entangled Knill–Laflamme–Milburn (KLM) states to Greenberger–Horne–Zeilinger (GHZ) states are proposed using weak cross‐Kerr nonlinearity and X‐quadrature homodyne measurement. Analyses show that the two‐qubit (Bell state) and three‐qubit conversion cases have very high fidelities and close‐to‐unity probabilities. The conversion processes are robust against photon loss. The schemes linking these two entangled states may be helpful to the study of quantum information processing based on them.
In the paper, we propose a protocol for the one-step interconversions between the Greenberger-Horne-Zeilinger (GHZ) states and the WWW states with deterministic success probabilities. The Rydberg interactions among three Rydberg atoms are utilized here to structure nonlocal operations for the interconversions. Additionally, we construct a Lewis-Riesenfeld invariant for a four-level system and afterwards use it to reversely design the Rabi frequencies of the effective Hamiltonian. The numerical simulations indicate that the protocol is robust against the spontaneous emission, the dephasing, the thermal noise, the systematic errors on Rabi frequencies, and the frequency mismatching. Therefore, the protocol may contribute to the research of the interconversions between entanglements.
Abstract In the process of quantum information processing, decoherence effect caused by the coupling between system and its environment will no doubt lead to the error of quantum information stored in the system. To decrease the influence of decoherence effect, decoherence‐free subspace (DFS) is introduced. In this work, several schemes to convert the polarized‐entangled Knill–Laflamme–Milburn (KLM) states into Greenberger–Horne–Zeilinger (GHZ) states in DFS by using the weak cross‐Kerr nonlinearity are proposed. Numerical analysis shows that the proposed schemes have high fidelity and success probability. Due to the unique applications of multi‐qubit quantum entangled states in quantum information processing and the robust feature of DFS, the proposed schemes may play positive roles in the future development of quantum communication and quantum information processing tasks.
Abstract Quantum entanglement plays a crucial role in quantum information technologies. In the paper, we propose two schemes to convert from two-photon Knill–Laflamme–Milburn (KLM) entangled states to Bell states and three-photon KLM state to Greenberger–Horne–Zeilinger states based on error-detected quantum devices (EDQDs), which employ the interaction between a quantum-dot-cavity system and a photon. Moreover, the quantum circuits of EDQDs applied in the conversion processes make our schemes carry out faithfully, as the practical photon-scattering deviations are changed into heralded-failure detections. Analyses show that conversion cases have unity fidelities and high efficiencies, which encourage us to appreciate deeply fundamental properties of entanglement.
We investigate the possibilities for a deterministic conversion between two important types of maximally entangled multiqubit states, namely, WWW and Greenberger-Horne-Zeilinger (GHZ) states, in the Rydberg-blockade regime of a neutral-atom system where each atom is subject to four external laser pulses. Such interconversions between WWW states and their GHZ counterparts have quite recently been addressed using the method of shortcuts to adiabaticity, more precisely techniques based on Lewis-Riesenfeld invariants [R.-H. Zheng et al., Phys. Rev. A 101, 012345 (2020)]. Motivated in part by this recent work, we revisit the WWW to GHZ state-conversion problem using a fundamentally different approach, which is based on the dynamical symmetries of the system and a Lie-algebraic parametrization of its permissible evolutions. In contrast to the previously used invariant-based approach, which leads to a state-conversion protocol characterized by strongly time-dependent Rabi frequencies of external lasers, ours can also yield one with time-independent Rabi frequencies. This feature makes our protocol more easily applicable experimentally, with the added advantage that it allows the desired state conversion to be carried out in a significantly shorter time with the same total laser pulse energy used.