  A quantum many-body system subject to unitary evolution and repeated local
measurements with an increasing rate undergoes a measurement-induced
entanglement transition from extensive (or subextensive) to area law entropy
scaling. We find that certain open boundary systems under "generalized
monitoring", consisting of "projective monitoring" and conditional feedback,
display an anomalous late-time particle concentration on the edge, reminiscent
of the "skin effect" in non-Hermitian systems. Such feedback-induced skin
effect will suppress the entanglement generation, rendering the system
short-range entangled without measurement-induced entanglement transition.
While initially emerged in noninteracting models, such skin effect can also
occur in chaotic interacting systems and Floquet quantum circuits subjected to
random generalized measurements. Since the dynamics of the skin effect do not
require post selection, and can be observed at the particle number level, the
phenomenon is experimentally relevant and accessible in noisy
intermediate-scale quantum platforms, such as trapped ions.
