Entanglement dynamics for qubits dissipating into a common environment

We provide an analytical investigation of the entanglement dynamics for a system composed of an arbitrary number of qubits dissipating into a common environment. Specifically, we consider product initial states with a given number of excitations whose evolution remains confined on low-dimensional subspaces of the operators space. We then find for which pairs of qubits entanglement can be generated and can persist at a steady state. Finally, we determine the stationary distribution of entanglement as well as its scaling versus the total number of qubits in the syste