  We experimentally test invariance properties of the six-photonic-qubits
generalization of a singlet state. Our results clearly corroborate with theory.
The invariance properties are useful to beat some types of decoherence. We also
experimentally detect entanglement in the state using an appropriate witness
observable, composed of local observables. Our results clearly indicate that
the tested setup, which is very stable, is a good candidate for realization of
various multi-party quantum communication protocols. The estimated fidelity of
the produced state is very high: it reveals very strong EPR six-photon
correlations of error rate below 6%.
