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Physical Review A

Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process

Jie Song, Xiudong Sun, Qing-Xia Mu, Lingli Zhang, Yan Xia, He‐Shan Song

Published Aug 30, 2013• 31 citations
Publisher

Abstract

We consider an open quantum system consisting of four atoms which are placed in a damped cavity. Through a dissipative dynamics process, a $W$ state can be converted into a Greenberger-Horne-Zeilinger state with deterministic probability. In addition, the interaction time need not be controlled strictly in the dynamics process. The protocol may open up a promising perspective for quantum state conversion between different classes of entanglement and cavity quantum electrodynamics systems.

DOI
10.1103/physreva.88.024305

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We consider an open quantum system consisting of four atoms which are placed in a damped cavity. Through a dissipative dynamics process, a WWW state can be converted into a Greenberger-Horne-Zeilinger state with deterministic probability. In addition, the interaction time need not be controlled strictly in the dynamics process. The protocol may open up a promising perspective for quantum state conversion between different classes of entanglement and cavity quantum electrodynamics systems.
Abstract State conversion between the Greenberger–Horne–Zeilinger (GHZ) state and the W state is a challenging open problem because these states cannot be converted to each other by just local operations and classical communication. Here we propose a cavity quantum electrodynamics method based on interference of polarized photons emitted by the atoms trapped in spatially separated optical cavities that can convert a three-atom W state to a GHZ state. We calculate the success probability and fidelity of the converted GHZ state when the cavity decay, spontaneous atomic decay and photon leakage of the cavities are taken into account for a practical system, which shows that the proposed scheme is feasible and within the reach of current experimental technology.
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.
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.
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.
We propose a specific method for converting a four-photon Greenberger-Horne-Zeilinger (GHZ) state to a W state in a deterministic way by using linear optical elements, cross-Kerr nonlinearities, and homodyne measurement. We consider the effects of the quadrature homodyne measurements on the fidelity of the W state and the experimental feasibility of the proposed scheme. This might provide great prospects for converting multipartite entangled states into each other for future optical quantum information processing (QIP).