and strong coupling regimes. So the GRWA works reasonably well in the ultra-strong coupling regime $g/\omega<0.3$ at resonance. Interestingly, the level crossing is present in both the GRWA results and the exact ones. The RWA requires weak coupling due to the complete neglect of the CRW terms, which are qualitatively incorrect as the coupling strength increases. So the GRWA includes the dominant contribution of the CRW terms, exhibiting substantial improvement of energy levels over the RWA one. The RWA fails in particular to describe the eigenstates, which should be more sensitive in the quantum entanglement presented in the next section.

Quantum entanglement
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In the present three-qubit system, we study the GME for the multipartite entanglement and the concurrence for the bipartite entanglement. A fully separable three-particle state must contain no entanglement. If the state is not fully separable, then it contains some entanglement, but it might be still separable with respect to two-party configurations. For genuine multiparticle entangled states, all particles are entangled and therefore GME is very important among various definition of entanglements.

We review the basic definitions of GME for the three qubits $A$, $B$, and $C$. A separable state is a mixture of product states with 