  We experimentally test the recently predicted anisotropic invariance
properties of pure three-qubit states, via generation and measurement of
polarisation-path entangled three-qubit states. These properties do not require
aligned reference frames and can be determined from measurements on any two of
the qubits. They have several applications, such as a universal ordering of
pairwise quantum correlations, strong monogamy relations for Bell inequalities
and quantum steering, and a complementarity relation for Bell nonlocality
versus 3-tangle, some of which we also test. The results indicate that
anisotropic invariance, together with the three qubit Bloch vector lengths, can
provide a robust and complete set of invariants for such states under local
unitary transformations.
