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Generic many-body systems coupled to an environment lose their quantumentanglement due to decoherence and evolve to a mixed state with only classicalcorrelations. Here, we show that measurements can stabilize quantumentanglement within open quantum systems. Specifically, in random unitarycircuits with dephasing at the boundary, we find both numerically andanalytically that projective measurements performed at a small nonvanishingrate results in a steady state with an $L^{1/3}$ power-law scaling entanglementnegativity within the system. Using an analytical mapping to a statisticalmechanics model of directed polymers in a random environment, we show that thepower-law negativity scaling can be understood as Kardar-Parisi-Zhangfluctuations due to the random measurement locations. Further increasing themeasurement rate leads to a phase transition into an area-law negativity phase,which is of the same universality as the entanglement transition in monitoredrandom circuits without decoherence.

Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit