# Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation

## TL;DR

This paper compares local and global master equations for coupled qubits interacting with baths, demonstrating that the global approach with partial secular approximation yields more accurate results in various quantum phenomena.

## Contribution

It provides a detailed derivation of the master equations and shows the superiority of the global approach with partial secular approximation over local methods.

## Key findings

- Global approach with partial secular approximation is more accurate.
- Global approach better predicts heat current, entanglement, and synchronization.
- Local approaches may be less reliable in certain regimes.

## Abstract

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, showing that they intrinsically depend on the way we 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-Markov approximations 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 by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.