  We analyse the minimum quantum resources needed to realise strong
non-locality, as exemplified e.g. by the classical GHZ construction. It was
already known that no two-qubit system, with any finite number of local
measurements, can realise strong non-locality. For three-qubit systems, we show
that strong non-locality can only be realised in the GHZ SLOCC class, and with
equatorial measurements. However, we show that in this class there is an
infinite family of states which are pairwise non-LU-equivalent that realise
strong non-locality with finitely many measurements. These states have
decreasing entanglement between one qubit and the other two, necessitating an
increasing number of local measurements on the latter.

Quantum Physics