  We address the problem of the persistence of entanglement of quantum light
under mode transformations, where orthogonal modes define the parties between
which quantum correlations can occur. Since the representation of a fixed
photonic quantum state in different optical mode bases can substantially
influence the entanglement properties of said state, we devise a constructive
method to obtain families of states with the genuine feature of remaining
entangled for any choice of mode decomposition. In the first step, we focus on
two-photon states in a bipartite system and optimize their entanglement
properties with respect to unitary mode transformations. Applying a necessary
and sufficient entanglement witness criteria, we are then able to prove that
the class of constructed states is entangled for arbitrary mode decompositions.
Furthermore, we provide optimal bounds to the robustness of the
mode-independent entanglement under general imperfections. In the second step,
we demonstrate the power of our technique by showing how it can be
straightforwardly extended to higher-order photon numbers in multipartite
systems, together with providing a generally applicable and rigorous definition
of mode-independent separability and inseparability for mixed states.
