  We study the entanglement effect of beam splitter on the temporally stable
phase states. Specifically, we consider the eigenstates (phase states) of an
unitary phase operator resulting from the polar decomposition of ladder
operators of generalized Weyl--Heisenberg algebras possessing finite
dimensional representation space. The linear entropy that measures the degree
of entanglement at the output of the beam splitter is analytically obtained. We
find that the entanglement is not only strongly dependent on the Hilbert space
dimension but also quite related to strength the parameter ensuring the
temporal stability of the phase states. Finally, we discuss the evolution of
the entangled phase states.
