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

TL;DR

This paper develops a theoretical framework to study how quantum entanglement evolves over time among superconducting qubits due to the dynamical Lamb effect, considering dissipation and different switching protocols, with potential for creating entangled states.

Contribution

It introduces a comprehensive model for entanglement dynamics in multi-qubit systems under dissipation and periodic coupling switching, including numerical analysis and entanglement measures.

Findings

Entanglement can be generated even with dissipation.

Different measures reveal varying details of entanglement.

Optimal parameters can maximize entanglement.

Abstract

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