  The compositional techniques of categorical quantum mechanics are applied to
analyse 3-qubit quantum entanglement. In particular the graphical calculus of
complementary observables and corresponding phases due to Duncan and one of the
authors is used to construct representative members of the two genuinely
tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely
illustrates the respectively pairwise and global tripartite entanglement found
in the W- and GHZ-class states. A new concept of supplementarity allows us to
characterise inhabitants of the W class within the abstract diagrammatic
calculus; these method extends to more general multipartite qubit states.
