  We report the discovery of two new invariants for three-qubit states which,
similarly to the 3-tangle, are invariant under local unitary transformations
and permutations of the parties. These quantities have a direct interpretation
in terms of the anisotropy of pairwise spin correlations. Applications include
a universal ordering of pairwise quantum correlation measures for pure
three-qubit states; tradeoff relations for anisotropy, 3-tangle and Bell
nonlocality; strong monogamy relations for Bell inequalities,
Einstein-Podolsky-Rosen steering inequalities, geometric discord and fidelity
of remote state preparation (including results for arbitrary three-party
states); and a statistical and reference-frame-independent form of quantum
secret sharing.
