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 $\mathrm{\Delta }$ and subject to continuous, on-site, spin-resolved charge measurements at rate $\gamma$. 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 $\mathrm{\Delta }>0$, the steady-state entanglement $S_s$ increases with $\gamma$ over a finite interval $0<\gamma <{\gamma }_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$. 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 $\mathrm{\Delta }>0$ and small but finite $\gamma$, the steady-state entanglement scales as $S_s\sim {\ln }^{2}L$. This implies that, in this setting, measurement-enhanced entanglement does not persist in the thermodynamic limit.