  We describe a method to detect twin-beam multiphoton entanglement based on a
beam splitter and weak nonlinearities. For the twin-beam four-photon
entanglement, we explore a symmetry detector. It works not only for collecting
two-pair entangled states directly from the spontaneous parametric
down-conversion process, but also for purifying them by cascading these
symmetry detectors. Surprisingly, by calculating the iterative coefficient and
the success probability we show that with a few iterations the desired two-pair
can be obtained from a class of four-photon entangled states. We then
generalize the symmetry detector to $n$-pair emissions and show that it is
capable of determining the number of the pairs emitted indistinguishably from
the spontaneous parametric down-conversion source, which may contribute to
explore multipair entanglement with a large number of photons.
