Geometry of two-body correlations in three-qubit states

TL;DR

This paper investigates the geometric constraints of two-body correlations in three-qubit states, deriving bounds, entanglement criteria, and state characterization methods using local-unitarily invariant measures.

Contribution

It introduces a geometric framework with invariant coordinates to analyze correlations, providing tight bounds and entanglement detection criteria for three-qubit states.

Findings

Derived tight nonlinear bounds for pure three-qubit states.

Extended bounds to include three-body correlations.

Proposed criteria for detecting multipartite entanglement and characterizing state rank.

Abstract

We study restrictions of two-body correlations in three-qubit states, using three local-unitarily invariant coordinates based on the Bloch vector lengths of the marginal states. First, we find tight nonlinear bounds satisfied by all pure states and extend this result by including the three-body correlations. Second, we consider mixed states and conjecture a tight non-linear bound for all three-qubit states. Finally, within the created framework we give criteria to detect different types of multipartite entanglement as well as characterize the rank of the quantum state.