  We consider Bell tests in which the distant observers can perform local
filtering before testing a Bell inequality. Notably, in this setup, certain
entangled states admitting a local hidden variable model in the standard Bell
scenario can nevertheless violate a Bell inequality after filtering, displaying
so-called hidden nonlocality. Here we ask whether all entangled states can
violate a Bell inequality after well-chosen local filtering. We answer this
question in the negative by showing that there exist entangled states without
hidden nonlocality. Specifically, we prove that some two-qubit Werner states
still admit a local hidden variable model after any possible local filtering on
a single copy of the state.
