Two coupled qubits interacting with a thermal bath: A comparative study of different models

We investigate the dynamics of two interacting two-level systems (qubits) having one of them isolated and the other coupled to a large number of modes of the quantized electromagnetic field (thermal reservoir). We consider two different models of system-reservoir interaction: (i) a “microscopic” model, according to which the corresponding master equation is derived taking into account the interaction between the two subsystems (qubits); (ii) a naive “phenomenological” model, in which such interaction is neglected in the derivation of the master equation. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit in both the strong and weak coupling regimes of the inter-qubit interaction. We also consider different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).