Measurement-enhanced entanglement in a monitored superconducting chain

TL;DR

This paper demonstrates that in a monitored superconducting fermionic chain, measurements can enhance entanglement by suppressing pairing correlations, leading to a non-monotonic relationship between measurement rate and entanglement.

Contribution

It reveals a novel phenomenon where measurements increase entanglement in a quantum chain, contrary to typical expectations, supported by simulations and analytical models.

Findings

Steady-state entanglement increases with measurement rate for certain parameters.

Pairing suppression by measurements leads to measurement-enhanced entanglement.

Entanglement scales as rac12; \u2212 rac12; \, ext{ln}^2 L in the steady state for small measurement rates.

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 $S_s$ increases with $\gamma$ over a finite interval $0<\gamma<\gamma_{\rm peak}$. 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 $\Delta>0$ 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.