  We investigate the emerging properties of quantum walks with temporal
disorder engineered from a binary Markov chain with tailored correlation, $C$,
and disorder strength, $r$. We show that when the disorder is weak -- $r \ll 1$
-- the introduction of negative correlation leads to a counter-intuitive higher
production of spin-lattice entanglement entropy, $S_e$, than the setting with
positive correlation, that is $S_e(-|C|)>S_e(|C|)$. These results show that
negatively correlated disorder plays a more important role in quantum
entanglement than it has been assumed in the literature.
