Unraveling-induced entanglement phase transition in diffusive trajectories of continuously monitored noninteracting fermionic systems

The competition between unitary quantum dynamics and dissipative stochastic effects, as emerging from continuous-monitoring processes, can culminate in measurement-induced phase transitions. Here, a many-body system abruptly passes, when exceeding a critical measurement rate, from a highly entangled phase to a low-entanglement one. We consider a different perspective on entanglement phase transitions and explore whether these can emerge when the measurement process itself is modified, while keeping the measurement rate fixed. To illustrate this idea, we consider a noninteracting fermionic system and focus on diffusive detection processes. Through extensive numerical simulations, we show that, upon varying a suitable \textit{unraveling parameter} -- interpolating between measurements of different quadrature operators -- the system displays a transition from a phase with area-law entanglement to one where entanglement scales logarithmically with the system size. Our findings may be relevant for tailoring quantum correlations in noisy quantum devices and for conceiving optimal classical simulation strategies.