title: Anisotropic Invariance and the Distribution of Quantum Correlations.
abstract: We report the discovery of two new invariants for three-qubit states which, similarly to the three-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; trade-off relations for anisotropy, three-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.
authors.affiliation: Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane QLD 4111, Australia.|Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
authors.forename: Shuming
authors.initials: S
authors.lastname: Cheng
authors.affiliation: Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane QLD 4111, Australia.
authors.forename: Michael J W
authors.initials: MJ
authors.lastname: Hall