  We study resonant CP-violating Einstein--Podolsky--Rosen correlations that
may take place in the production and decay of unstable scalar particles at
high-energy colliders. We show that as a consequence of unitarity and CPT
invariance of the S-matrix, in 2 --> 2 scatterings mediated by mixed scalar
particles, at least three linearly independent decay matrices associated with
the unstable scalar states are needed to obtain non-zero CP-odd observables
that are also odd under C-conjugation. Instead, for the correlated production
and decay of two unstable particle systems in 2 --> 4 processes, we find that
only two independent decay matrices are sufficient to induce a net
non-vanishing CP-violating phenomenon. As an application of this theorem, we
present numerical estimates of CP asymmetries for the correlated production and
decay of supersymmetric scalar top--anti-top pairs at the LHC, and demonstrate
that these could reach values of order one. As a byproduct of our analysis, we
develop a novel spinorial trace technique, which enables us to efficiently
evaluate lengthy expressions of squared amplitudes describing the resonant
scalar transitions.
