  Invariant entangled states remain unchanged under simultaneous identical
unitary transformations of all their subsystems. We experimentally generate and
characterize such invariant two-, four-, and six-photon polarization entangled
states. This is done only with a suitable filtering procedure of multiple
emissions of entangled photon pairs from a single source, without any
interferometric overlaps. We get the desired states utilizing bosonic emission
enhancement due to indistinguishability. The setup is very stable, and gives
high interference contrasts. Thus, the process is a very likely candidate for
various photonic demonstrations of quantum information protocols.
