  Information propagation in the one-dimensional infinite temperature Hubbard
model with a dissipative particle sink at the end of a semi-infinite chain is
studied. In the strongly interacting limit, the two-site mutual information and
the operator entanglement entropy exhibit a rich structure with two propagating
information fronts and superimposed interference fringes. A classical
reversible cellular automaton model quantitatively captures the transport and
the slow, classical part of the correlations, but fails to describe the rapidly
propagating information jet. The fast quantum jet resembles coherent free
particle propagation, with the accompanying long-ranged interference fringes
that are exponentially damped by short-ranged spin correlations in the
many-body background.
