  We prove that there is no finite-alphabet nonlocal box that generates exactly
those correlations that can be generated using a maximally entangled pair of
qubits. More generally, we prove that if some finite-alphabet nonlocal box is
strong enough to simulate arbitrary local projective measurements of a
maximally entangled pair of qubits, then that nonlocal box cannot itself be
simulated using any finite amount of entanglement. We also give a quantitative
version of this theorem for approximate simulations, along with a corresponding
upper bound.
