  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.
