  We study state engineering through bilinear interactions between two remote
qubits and two-mode Gaussian light fields. The attainable two-qubit states span
the entire physically allowed region in the entanglement-versus-global-purity
plane. Two-mode Gaussian states with maximal entanglement at fixed global and
marginal entropies produce maximally entangled two-qubit states in the
corresponding entropic diagram. We show that a small set of parameters
characterizing extremally entangled two-mode Gaussian states is sufficient to
control the engineering of extremally entangled two-qubit states, which can be
realized in realistic matter-light scenarios.
