  Correlations in multiparticle systems are constrained by restrictions from
quantum mechanics. A prominent example for these restrictions are monogamy
relations, limiting the amount of entanglement between pairs of particles in a
three-particle system. A powerful tool to study correlation constraints is the
notion of sector lengths. These quantify, for different $k$, the amount of
$k$-partite correlations in a quantum state in a basis-independent manner. We
derive tight bounds on the sector lengths in multi-qubit states and highlight
applications of these bounds to entanglement detection, monogamy relations and
the $n$-representability problem. For the case of two- and three qubits we
characterize the possible sector lengths completely and prove a symmetrized
version of strong subadditivity for the linear entropy.
