  In a recent paper, Q. M\'erigot proved that representations in SO(2,n) of
uniform lattices of SO(1,n) which are Anosov in the sense of Labourie are
quasi-Fuchsian, i.e. are faithfull, discrete, and preserve an acausal subset in
the boundary of anti-de Sitter space. In the present paper, we prove the
reverse implication. It also includes: -- A construction of Dirichlet domains
in the context of anti-de Sitter geometry, -- A proof that spatially compact
globally hyperbolic anti-de Sitter spacetimes with acausal limit set admit
locally CAT(-1) Cauchy hypersurfaces.
