  Assume Alice and Bob share some bipartite $d$-dimensional quantum state. A
well-known result in quantum mechanics says that by performing two-outcome
measurements, Alice and Bob can produce correlations that cannot be obtained
locally, i.e., with shared randomness alone. We show that by using only two
bits of communication, Alice and Bob can classically simulate any such
correlations. All previous protocols for exact simulation required the
communication to grow to infinity with the dimension $d$. Our protocol and
analysis are based on a power series method, resembling Krivine's bound on
Grothendieck's constant, and on the computation of volumes of spherical
tetrahedra.
