  We study the transport properties of quantum 1D systems under strong
monitoring. The quantum Zeno effect inhibits transport and induces
localization. Beyond the Zeno freezing and on long time scales, a new dynamics
emerges in the form of a Markov process. Studying fermionic and bosonic chains
under strong monitoring, we are able to identify the quantum origin of the
classical exclusion process, inclusion process and a sub-class of the
misanthrope process. Moreover, we show that passive monitoring cannot break
time-reversal symmetry and that the transport generally loses its ballistic
nature existing for weak measurements.
