  We propose a scheme for conditional implementation of a quantum phase gate by
using distant atoms trapped in different optical cavities. Instead of direct
interaction between atoms, the present scheme makes use of quantum interference
of polarized photons decaying from the optical cavities to conditionally create
the desired quantum phase gate between two distant atoms. The proposed scheme
only needs linear optical elements and a two-fold coincidence detection, and
are insensitive to the quantum noise. The scheme can be directly used to
prepare any quantum state of many distant atoms.
