Measurement-enhanced entanglement in a monitored superconducting chain

Abstract

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 $\Delta$ 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 $\Delta >0$, the steady-state entanglement ${\mathcal{S}}_s$ increases with $\gamma$ over a finite interval $0<\gamma <{\gamma }_{\mathrm{peak}}$. 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 $\Delta >0$ and small but finite $\gamma$, the steady-state entanglement scales as ${\mathcal{S}}_s(L)\sim {\ln }^{2}L$. This implies that, in this setting, measurement-enhanced entanglement does not persist in the thermodynamic limit.

arXiv comment5 pages of main text (4 figures) and 9 pages of supplemental material (2 figures); companion paper to arXiv:2607.07835. Comments are welcome