Symmetry-Controlled Criticality and Zeno Localization in a Monitored Quasiperiodic Superconductor

Measurement-induced transitions of free fermions depend strongly on symmetry, but their interplay with quasiperiodic localization and superconducting pairing remains largely unexplored. We study a continuously monitored model of free fermions with pairing, where quasiperiodicity both controls localization and changes the symmetry class of the monitored field theory. Using topological entanglement entropy as a probe of nonlocal correlations in quantum state diffusion simulations, we identify a transition between a critical phase whose von Neumann entanglement entropy scales as (ln L)² and an area-law phase, whereas no transition occurs in the clean limit, consistent with the corresponding DIII and D nonlinear sigma models. The transition line exhibits strong multifractality and depends nonmonotonically on quasiperiodicity, which we associate with the symmetry crossover. Deep in the Zeno regime, we derive an effective non-Hermitian Bogoliubov-de Gennes description of individual trajectories and obtain a closed-form localization length that quantitatively agrees with numerics. Our results reveal how symmetry, quasiperiodic localization, and measurement backaction combine to determine both critical entanglement and microscopic trajectory localization in monitored superconductors.