  Non-local correlations between a fully characterised quantum system and an
untrusted black box device are described by an assemblage of conditional
quantum states. These assemblages form a convex set, whose extremal points are
relevant in many operational contexts. We give necessary and sufficient
conditions for an assemblage to be extremal using linear independence
conditions, and an algorithm to decompose a generic assemblage into extremal
points. A Matlab implementation of this algorithm is provided in the
supplementary material.
