We explore the phase space quantum effects, quantum coherence and non-classicality, for two
coupled identical qubits with intrinsic decoherence. The two qubits are in a nonlinear interaction
with a quantum field via an intensity-dependent coupling. We investigate the non-classicality via the
Wigner functions. We also study the phase space information and the quantum coherence via the
Q-function, Wehrl density, and Wehrl entropy. It is found that the robustness of the non-classicality
for the superposition of coherent states, is highly sensitive to the coupling constants. The phase space
quantum information and the matter-light quantum coherence can be controlled by the two-qubit
coupling, initial cavity-field and the intrinsic decoherence