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Physical Review A

Deterministic interconversions between the Greenberger-Horne-Zeilinger states and the W states by invariant-based pulse design

Ri‐Hua Zheng, Yi‐Hao Kang, Du Ran, Zhi‐Cheng Shi, Yan Xia

Published Jan 28, 2020• 52 citations
Publisher

Abstract

In the paper, we propose a protocol for the one-step interconversions between the Greenberger-Horne-Zeilinger (GHZ) states and the $W$ 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.

DOI
10.1103/physreva.101.012345

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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 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.
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.
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.
We investigate the possibilities for a deterministic conversion between two important types of maximally-entangled multiqubit states -- namely, W 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 W 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 {\em et al.}, Phys. Rev. A {\bf 101}, 012345 (2020)]. Motivated in part by this recent work, we revisit the W-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.
In this paper, we propose a protocol to realize the conversions between Greenberger-Horne-Zeilinger (GHZ) states and WWW states of spin qubits. By analyzing and simplifying the dynamics of the system, the control fields are designed via the inverse Hamiltonian engineering based on the Lie transforms. Moreover, the states' conversions between multitype GHZ states and WWW states can be executed deterministically and reversibly, which makes the protocol resource saving and flexible. We show in numerical simulations that the state conversions are robust against the systematic errors, random noise, and frequency mismatching of the control fields. Therefore, the protocol may provide some useful prospectives to the research of quantum mechanics and applications of quantum information processing based on GHZ states and WWW states.
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.