Anisotropic invariance and the distribution of quantum correlations

TL;DR

This paper introduces two new invariants for three-qubit states related to anisotropy in spin correlations, providing insights into quantum correlation measures, monogamy relations, and quantum secret sharing.

Contribution

The paper discovers two new invariants for three-qubit states that relate to anisotropy and are invariant under local unitaries and permutations, expanding understanding of quantum correlations.

Findings

Universal ordering of pairwise quantum correlation measures

Tradeoff relations involving anisotropy, 3-tangle, and Bell nonlocality

Strong monogamy relations for various quantum inequalities

Abstract

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.