Open systems ofcoupled 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, manyefforts have been made toward the possibility ofemploying local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason maybe 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, showing that they intrinsically depend on the waywe apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born–Markovapproximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated bya common bath, and the emergence ofspontaneous synchronization, showing the importance ofthe accurate choice ofapproach.
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