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arXiv:2104.12341 · SciPost Physics

GHZ-like states in the Qubit-Qudit Rabi model

Yuan Shen, Giampiero Marchegiani, Gianluigi Catelani, Luigi Amico A, A. Q. Liu, W. J. Fan, L. C. Kwek

Published Dec 1, 2021• 4 citations
arXivHTMLPDF

Abstract

We study a Rabi type Hamiltonian system in which a qubit and a d d -level quantum system (qudit) are coupled through a common resonator. In the weak and strong coupling limits the spectrum is analysed through suitable perturbative schemes. The analysis show that the presence of the multilevels of the qudit effectively enhance the qubit-qudit interaction. The ground state of the strongly coupled system is found to be of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the qubit-qudit strong coupling, the nature of the specific tripartite entanglement of the GHZ state suppresses the bipartite entanglement. We analyze the system dynamics under quenching and adiabatic switching of the qubit-resonator and qudit-resonator couplings. In the quench case, we found that the non-adiabatic generation of photons in the resonator is enhanced by the number of levels in the qudit. The adiabatic control represents a possible route for preparation of GHZ states. Our analysis provides relevant information for future studies on coherent state transfer in qubit-qudit systems.

DOI
10.21468/scipostphys.11.6.099

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We study a Rabi type Hamiltonian system in which a qubit and a d d -level quantum system (qudit) are coupled through a common resonator. In the weak and strong coupling limits the spectrum is analysed through suitable perturbative schemes. The analysis show that the presence of the multilevels of the qudit effectively enhance the qubit-qudit interaction. The ground state of the strongly coupled system is found to be of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the qubit-qudit strong coupling, the nature of the specific tripartite entanglement of the GHZ state suppresses the bipartite entanglement. We analyze the system dynamics under quenching and adiabatic switching of the qubit-resonator and qudit-resonator couplings. In the quench case, we found that the non-adiabatic generation of photons in the resonator is enhanced by the number of levels in the qudit. The adiabatic control represents a possible route for preparation of GHZ states. Our analysis provides relevant information for future studies on coherent state transfer in qubit-qudit systems.
The generation of multipartite entangled states is fundamental tool for a wide range of quantum information processing tasks, including teleportation, superdense coding, and quantum key distributions. This work demonstrates a scheme for high-fidelity Greenberger–Horne–Zeilinger (GHZ) and W states in a weakly coupled resonator- qubit-resonator system by exploiting quantum destructive interference and strategically suppresses higher-order transition pathways in the joint photonic Fock space to enable controlled and efficient tripartite entanglement.
Entanglement refers to the inability of many-body quantum mechanical systems to be separated into independent subsystems. This has been well investigated in systems consisting of two entangled subsystems. In larger systems, more complex types of entanglement exist. In a system consisting of three subsystems (e.g., qubits), it is possible that all three subsystems are entangled with each other in a way that cannot be reduced to bipartite entanglement, and it is known that two different, inequivalent forms of tripartite entanglement exist such as the GHZ and WWW states (GHZ denotes ``Greenberger-Horne-Zeilinger''). Here, we investigate a particularly interesting system with competing one-, two-, and three-body interactions. Its ground state can be a product state, a GHZ state, or a WWW state, depending on the type and strength of the spin-spin couplings. By varying an external control parameter, the system can be made to undergo quantum transitions between the various ground-state-entanglement phases. We implement the system in an NMR quantum simulator and use adiabatic evolution of the effective Hamiltonian to drive the system through the quantum transitions. In the experimental and numerical simulations, we check the suitability of different observables for making the quantum transitions visible and for characterizing the different phases.
Hybrid entanglement between particlelike and wavelike optical qubits has drawn increasing attention because such hybrid entanglement is a key resource in establishing hybrid quantum networks and connecting quantum processors with different encoding qubits. For convenience, we define ``particlelike optical qubits'' as PO qubits and ``wavelike optical qubits'' as WO qubits. In this work, we propose a method to create a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state of nnn PO qubits and nnn WO qubits, by using 2n2n2n microwave cavities coupled to a superconducting flux qutrit. The two logic states of a PO qubit here are represented by the vacuum state and the single-photon state of a cavity (or represented by the rotated states of the vacuum state and the single-photon state), while the two logic states of a WO qubit are indicated by the two coherent states of a cavity. The procedure for preparing the GHZ state consists of only a few basic operations, and the circuit resources are significantly reduced because of using only one flux qutrit as the coupler. The GHZ-state preparation time does not depend on the number of qubits, and the GHZ state is deterministically generated since no measurement is made. In addition, the intermediate higher-energy level of the qutrit during the entire operation is virtually excited and thus decoherence from this level is greatly suppressed. This proposal is quite general and can be extended to create the proposed hybrid GHZ state, by using a $\mathrm{\ensuremath{\Lambda}}$-type natural or artificial atom coupled to 2n2n2n microwave or optical cavities. As an example, our numerical simulation demonstrates that within current circuit-QED technology, the hybrid GHZ state of two PO qubits and two WO qubits can be prepared with a high fidelity.
Abstract This study investigates the entanglement dynamics of the two-qubit quantum Rabi model (QRM) with both homogeneous and inhomogeneous couplings using the adiabatic approximation. The quantized field is initially prepared in a coherent state, while a separable state and a maximally entangled Bell state are selected as the initial two-qubit states. We characterize distinct types of entanglement generated among the subsystems through qubit–field interactions, with a focus on the bipartite entanglement between a single qubit and the field. Building on this, we examine tripartite correlations through the I -residual tangle, a measure that conclusively verifies the presence of genuine tripartite entanglement among the two qubits and the field. This work provides insights into the generation of tunable multipartite entanglement and the detection of quantum phase transitions in light–matter systems, such as circuit quantum electrodynamics (QED).
In this paper, we present a proof of principle of the formation of pure maximally entangled states from the Greenberger-Horne-Zeilinger (GHZ) class, in the experimental context of charged quantum dots. Each qubit must be identified as a pair of quantum dots, sharing an excess electron, coupled by tunneling. The electron-electron interaction is accounted for and is responsible for the coupling between the qubits. The interplay between coherent tunneling events and many-body interaction gives rise to the formation of highly entangled states. We begin by treating the problem of encoding three qubits in a system with three pairs of quantum dots, and the numerical analysis of the exact quantum dynamics to find the conditions for the generation of the GHZ states. An effective two-level model sheds light on the role of a high-order tunneling process behind the dynamics. The action of the main decoherence process, the charge dephasing, is quantified in the process. We then evaluate the physical requirements for the dynamical generation of GHZ states in an NNN-qubit scenario, and its challenges.