  We theoretically investigate the production of polarization-entangled photons
through the biexciton cascade decay in a single semiconductor quantum dot. In
the intermediate state the entanglement is encoded in the polarizations of the
first emitted photon and the exciton, where the exciton state can be
effectively ``measured'' by the solid state environment through the formation
of a lattice distortion. We show that the resulting loss of entanglement
becomes drastically enhanced if the phonons contributing to the lattice
distortion are subject to elastic scatterings at the device boundaries, which
might constitute a serious limitation for quantum-dot based entangled-photon
devices.
