  We present a way for entanglement purification based on two parametric
down-conversion (PDC) sources with cross-Kerr nonlinearities. It is comprised
of two processes. The first one is a primary entanglement purification protocol
for PDC sources with nondestructive quantum nondemolition (QND) detectors by
transferring the spatial entanglement of photon pairs to their polarization. In
this time, the QND detectors act as the role of controlled-not (CNot) gates.
Also they can distinguish the photon number of the spatial modes, which
provides a good way for the next process to purify the entanglement of the
photon pairs kept more. In the second process for entanglement purification,
new QND detectors are designed to act as the role of CNot gates. This protocol
has the advantage of high yield and it requires neither CNot gates based on
linear optical elements nor sophisticated single-photon detectors, which makes
it more convenient in practical applications.
