Enhanced entanglement negativity in boundary-driven monitored fermionic chains

We investigate entanglement dynamics in continuously monitored open quantum systems featuring current-carrying nonequilibrium states. focus on a prototypical one-dimensional model of boundary-driven noninteracting fermions with monitoring the local density, whose average Lindblad features well-studied ballistic to diffusive crossover transport. Here we analyze fermionic negativity, mutual information, and purity along different trajectories. show that this system enhances its negativity at long times, which otherwise decays zero absence measurements. This result is contrast case unitary evolution where suppresses production. For small values $\ensuremath{\gamma}$, stationary-state shows logarithmic scaling size, transitioning an area-law as $\ensuremath{\gamma}$ increased beyond critical value. Similar behavior found while late-time no apparent signature transition, being $O(1)$ for all $\ensuremath{\gamma}$. Our work unveils double role weak current-driven systems, simultaneously damping transport enhancing entanglement.