  We study in detail the generation and relaxation of quantum coherences
(entanglement) in a system of coupled polariton traps. By exploiting a Lie
algebraic based super-operator technique we provide an analytical exact
solution for the Markovian dissipative dynamics (Master equation) of such
system which is valid for arbitrary cluster size, polariton-polariton
interaction strength, temperature and initial state. Based on the exact
solution of the Master equation at T=0K, we discuss how dissipation affects the
quantum entanglement dynamics of coupled polariton systems.
