  Building on the Pusey-Barrett-Rudolph theorem, we derive a no-go theorem for
a vast class of deterministic hidden-variables theories, including those
consistent on their targeted domain. The strength of this result throws doubt
on seemingly natural assumptions (like the "preparation independence" of the
Pusey-Barrett-Rudolph theorem) about how "real states" of subsystems compose
for joint systems in nonentangled states. This points to constraints in
modeling tensor-product states, similar to constraints demonstrated for more
complex states by the Bell and Bell-Kochen-Specker theorems.
