  The notion of strong nonlocality, which refers to local irreducibility of a
set of orthogonal multipartite quantum states across each bipartition of the
subsystems, was put forward by Halder et al. in [Phys. Rev. Lett. 122, 040403
(2019)]. Here, we show the existence of three orthogonal quantum states in
(C^2)^{\otimes N} that cannot be perfectly distinguished locally across any
bipartition of the subsystems. Specifically, all these three states are
genuinely entangled, among which two are the N-qubit GHZ pairs. Since any three
locally indistinguishable states are always locally irreducible, the three
N-partite orthogonal states we present are strongly nonlocal. Thus, the
caridnality of strongly nonlocal sets here is dramatically smaller than all
known ones.
