  We theoretically investigate the production of polarization-entangled photons
through the biexciton cascade decay in a single semiconductor quantum dot. To
accomplish a high degree of entanglement, despite the exciton finestructure
splitting, one must either energetically align the two exciton states by means
of external fields or erase the which-path information by post-selecting
photons within the correct frequency range. Here we show that in the latter
scheme, as well as in related proposals, the photon state becomes deteriorated
through dephasing processes in the solid, and the degree of entanglement
remains low despite filtering.
