  We discuss the generation of states close to the boundary-family of maximally
entangled mixed states as defined by the use of concurrence and linear entropy.
The coupling of two qubits to a dissipation-affected bosonic mode is able to
produce a bipartite state having, for all practical purposes, the entanglement
and purity properties of one of such boundary states. We thoroughly study the
effects that thermal and squeezed character of the bosonic mode have in such a
process and we discuss tolerance to qubit phase-damping mechanisms. The
non-demanding nature of the scheme makes it realizable in a matter-light based
physical set-up, which we address in some details.
