Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
Cattaneo, Marco; Giorgi, Gian Luca; Maniscalco, Sabrina; Zambrini, Roberta
Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, proving that they intrinsically depend on the way we apply the secular approximation. Contrary to part of the previous literature that claims the failure of the global approach with secular approximation for small coupling constants, our results show that the global approach with partial secular approximation always provides the most accurate choice for the master equation. The full secular approximation may crash in some scenarios, depending not only on the coupling constant as previously thought, but also on the qubit detuning and on the difference between separate and common bath.