  Semiconductor quantum dots are promising sources for polarization-entangled
photons. As an alternative to the usual cascaded biexciton-exciton emission,
direct two-photon emission from the biexciton can be used. With a high-quality
optical resonator tuned to half the biexciton energy, a large proportion of the
photons can be steered into the two-photon emission channel. In this case the
degree of polarization entanglement is inherently insensitive to the exciton
fine-structure splitting. In the present work we analyze the biexciton emission
with particular emphasis on the influence of coupling of the quantum-dot cavity
system to its environment. Especially for a high-quality cavity, the coupling
to the surrounding semiconductor material can open up additional
phonon-assisted decay channels. Our analysis demonstrates that with the cavity
tuned to half the biexciton energy, the potentially detrimental influence of
the phonons on the polarization entanglement is strongly suppressed -- high
degrees of entanglement can still be achieved. We further discuss spectral
properties and statistics of the emitted twin photons.
