  In the present paper, we study the relation between criticality and
information transmission in the one-dimensional contact process with infection
parameter $\lambda .$ To do this we define the {\it sensitivity} of the process
to its initial condition. This sensitivity increases for values of $\lambda <
\lambda_c, $ the value of the critical parameter. The main point of the present
paper is that we show that actually it continues increasing even after $
\lambda_c $ and only starts decreasing for sufficiently large values of
$\lambda .$ This provides a counterexample to the common belief that associates
maximal information transmission to criticality.
