Measurement-enhanced entanglement in a monitored superconducting chain

A common view in monitored quantum dynamics is that local measurements suppress entanglement growth. We show that this intuition can fail in a one-dimensional spinful fermionic chain governed by a BCS Hamiltonian with pairing strength Δ and subject to continuous, on-site, spin-resolved charge measurements at rate γ. Using free-fermion simulations and quasiparticle analysis, we show that pairing suppresses entanglement growth, while measurements suppress pairing. Their competition yields measurement-enhanced entanglement: for Δ>0, the steady-state entanglement S_s increases with γ over a finite interval 0<γ<γ_{rm peak}. This occurs because stronger measurements suppress pairing correlations, which would otherwise suppress entanglement growth. Using a nonlinear sigma-model calculation and free-fermion simulations, we provide evidence that for Δ>0 and small but finite γ, the steady-state entanglement scales as S_ssim ln² L. This implies that, in this setting, measurement-enhanced entanglement does not persist in the thermodynamic limit.