  Recently de La Torre et al. [1] reconstructed Quantum Theory from its local
structure on the basis of local discriminability and the existence of a
one-parameter group of bipartite transformations containing an entangling gate.
This result relies on universality of an entangling gate for quantum
computation. Here we prove universality of C-NOT with local gates for Real
Quantum Theory (RQT), showing that such universality would not be sufficient
for the result, whereas local discriminability and the qubit structure play a
crucial role. For reversible computation, generally an extra rebit is needed
for RQT. As a byproduct we also provide a short proof of universality of C-NOT
for CQT.
