  If there is CPT violation, the nature of entanglement for neutral meson pairs
produced in meson factories may, on general grounds, be affected. The new form
of entanglement is the omega effect. Gravitational decoherence, due to
space-time foam, may be one route for deviations from CPT invariance. Two
models of space-time foam are considered. One, based on non-critical string
theory, is able to produce the new correlations in a natural way. The other,
based on the paradigm of thermal-like baths, is shown to be surprisingly
resistant to producing the effect even on exercising a total freedom of choice
for the state of the bath
