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A theoretical framework to investigate the time evolution of the quantumentanglement due to the dynamical Lamb effect between $N$ superconductingqubits coupled to a coplanar waveguide in the presence of different sources ofdissipation is developed. We quantitatively analyze the case of $N=2$ and $3$qubits under the assumptions of single switching of the coupling and absence ofdissipation within a perturbative approach. The same systems are analyzed forthe general case of periodic switching of the coupling in the presence ofdissipation via numerical calculations. Different measures of entanglementcompatible with mixed states are adopted. It is demonstrated that the differentmeasures show different level of details of the latter. The concurrence and thenegativity are obtained in the two qubits case, the three-$\pi$ and thenegativity in the three qubits case. It is shown that time-dependentGreenberger-Horne-Zeilinger states can be created even in presence ofdissipation. To maximize the quantum entanglement between the qubits, theeffects of tuning several parameters of the system are investigated.

Time evolution of the quantum entanglement between $N$ qubits due to dynamical Lamb effect in the presence of dissipation