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We use a noisy signal with finite correlation time to drive a spin(dissipative impurity) in the quantum XY spin chain and calculate the dynamicsof entanglement entropy of a bipartition of spins, for a stochastic quantumtrajectory. We compute the noise averaged entanglement entropy of a bipartitionof spins and observe that its speed of spreading decreases at strongdissipation, as a result of the Zeno effect. We recover the Zeno crossover andshow that noise averaged entanglement entropy can be used as a proxy for theheating and Zeno regimes. Upon increasing the correlation time of the noise,the location of the Zeno crossover shifts at stronger dissipation, extendingthe heating regime.

Zeno crossovers in the entanglement speed of spin chains with noisy impurities