  We show that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality
can be demonstrated in a certain kind of Bell experiment for all bipartite
entangled states. Our protocol allows local filtering measurements and involves
shared ancilla states that do not themselves violate CHSH. Our result follows
from two main steps. We first provide a simple characterization of the states
that violate the CHSH-inequality after local filtering operations in terms of
witness-like operators. Second, we prove that for each entangled state
$\sigma$, there exists another state $\rho$ not violating CHSH, such that
$\rho\otimes\sigma$ violates CHSH. Hence, in this scenario, $\sigma$ cannot be
substituted by classical correlations without changing the statistics of the
experiment; we say that $\sigma$ is not simulable by classical correlations and
our result is that entanglement is equivalent to non-simulability.
