  Measurement-induced phase transitions are the subject of intense current
research, both from an experimental and a theoretical perspective. We explore
the concept of implementing quantum measurements by coupling a many-body
lattice system to an ancillary degree of freedom (implemented using two
additional sites), on which projective measurements are performed. We analyze
the effect of repeated (``stroboscopic'') measurements on the dynamical
correlations of interacting hard-core bosons in a one-dimensional chain. An
important distinctive ingredient of the protocol is the fact that the detector
ancillas are not re-initialized after each measurement step. The detector thus
maintains memory of the accumulated influence by the measured correlated
system. Initially, we consider a model in which the ancilla is coupled to a
single lattice site. This setup allows obtaining information about the system
through Rabi oscillations in the ancillary degrees of freedom, modulated by the
ancilla-system interaction. The statistics of quantum trajectories exhibits a
``quantum-Zeno-valve effect'' that occurs when the measurement becomes strong,
with sharp branching between low and high entanglement. We proceed by extending
numerical simulations to the case of two ancillas and, then, to measurements on
all sites. With this realistic measurement apparatus, we find evidence of a
disentangling-entangling measurement-induced transition as was previously
observed in more abstract models. The dynamics features a broad distribution of
the entanglement entropy.
