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Chinese Physics B

Bipartite and tripartite entanglement in the two-qubit quantum Rabi model

毛丽君, Hongmei 红梅 Wang 王, Yaoyao Zhou, Hui 辉 Guo 郭

Published Jul 3, 2026• 0 citations
Publisher

Abstract

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).

DOI
10.1088/1674-1056/ae85f7

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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).
By means of composite quantum collision models, we study the entanglement dynamics of a bipartite system, i.e., two qubits S 1 and S 2 interacting directly with an intermediate auxiliary qubit S A, while S A is in turn coupled to a thermal reservoir. We are concerned with how the intracollisions of the reservoir qubits influence the entanglement dynamics. We show that even if the system is initially in the separated state, their entanglement can be generated due to the interaction between the qubits. In the long-time limit, the steady-state entanglement can be generated depending on the initial state of S 1 and S 2 and the environment temperature. We also study the dynamics of tripartite entanglement of the three qubits S 1, S 2, and S A when they are initially prepared in the GHZ state and separated state, respectively. For the GHZ initial state, the tripartite entanglement can be maintained for a long time when the collision strength between the environment qubits is sufficiently large.
’We investigate entanglement in an open quantum system, specifically in bipartite and tripartite systems of two dimensions for weak and strong fields based on numerical calculations. We address a systematic approach in calculating a tripartite entanglement using concurrence as a measure of entanglement based on a direct detection scheme (quantum jump method - with and without knowledge of which qubit jumps). We are also numerically calculating entanglement when one can and the ’Three-way tangle’ or ’Residual Entanglement’ approaches. We present significant differences of the concurrences of the various bipartite splits among the results of two ways of direct detection scheme and when a phase is introduced in the coupling term of the energy.
We analyze the dynamics of the quantum Rabi model for two qubits interacting through a common bosonic field (resonator), focusing on the generation and detection of maximally entangled states. We obtain analytical results for the unitary dynamics of this system in the slow-qubit (or degenerate) regime, considering ultra-strong coupling between qubits and resonator mode, for which the rotating wave approximation (RWA) is no longer applicable. We also numerically investigate the dynamics beyond the slow-qubit condition in order to study the validity of the model in the presence of less strict conditions.
The tripartite quantum Rabi model couples two qubits to a bosonic mode through a collective spin-oscillator interaction, providing a simple setting for studying two-qubit entanglement. In the zero-detuning limit, the triplet part of the spectrum splits into branches with zero and maximal entanglement, while the antisymmetric singlet ladder remains exactly decoupled. Within the triplet sector, finite detuning turns the crossings between these branches into avoided crossings and redistributes this entanglement. We identify an eigenbranch whose entanglement grows from nearly zero to a nearly maximal value through such avoided-crossing mixing. The weak-coupling level ordering yields a simple analytic criterion for whether this eigenbranch has a separable weak-coupling endpoint. A three-state effective model explains how the Bell-state component becomes dominant as the coupling increases. We further use a finite-time linear ramp of the collective coupling to benchmark the final coupling and ramp time required for high Bell-state fidelity. These results show how collective spin-oscillator coupling reorganizes spectral entanglement and connects static branch structure to finite-time Bell-state preparation.
We analyze the dynamics of the quantum Rabi model for two qubits interacting through a common bosonic field (resonator), focusing on the generation and detection of maximally entangled states. We obtain analytical results for the unitary dynamics of this system in the slow-qubit (or degenerate) regime, considering ultra-strong coupling between qubits and resonator mode, for which the rotating wave approximation (RWA) is no longer applicable. We also numerically investigate the dynamics beyond the slow-qubit condition in order to study the validity of the model in the presence of less strict conditions.
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.