  We consider devices with two inputs and two outputs, Alice and Bob each
having access to one input and one output. To such a device we associate
time-reverses by exchanging the roles of the inputs and the outputs. We find
that there are devices which admit a local hidden variable representation, but
for which time-reverses enable perfect signaling between Alice and Bob. That
is, a `perfect channel in one time direction' becomes a `non-channel in the
other direction'. Also, for PR boxes time-reverses enable signaling between
Alice and Bob, but never as a perfect channel. These results undermine the
representation of causal structures as partial orders or similar
`time-symmetric structures', as is often assumed in search of a theory of
quantum gravity. They also provide new insights into the structure of the
polytope of generalized probabilistic correlations, and contribute to the
growing area of research into quantum information processing in relativistic
spacetimes.
