Range-controlled entanglement in Lindbladian skin states of monitored fermions

Reservoir engineering can stabilize states inaccessible to unitary dynamics. Directed particle-conserving dissipation creates Lindbladian skin states, where Pauli exclusion turns edge accumulation into a many-body density imbalance. In a monitored fermion chain with tunable hopping range, we identify, within a Gaussian trajectory approximation, two finite-size scaling regimes: short-range hopping is consistent with complete skin accumulation and area-law entanglement, whereas sufficiently long-range hopping produces a finite bulk tail and effective algebraic sub-volume-law entanglement. Dissipation and coherent hopping thus jointly control skin localization and quantum entanglement, highlighting their close interconnection.