Entanglement negativity and measurement-induced phases in open quantum circuits

Recent works on monitored random quantum circuits have revealed a dynamical phase transition between volume law and area law entangled steady states. To determine whether large scale entanglement and measurement-induced transitions can survive in the presence of realistic decoherence processes, we investigate how these measurement-induced phases are affected by coupling to dephasing channels at the system boundaries. We employ the logarithmic negativity as a metric of mixed-state entanglement in the resulting open system dynamics, where the bipartite entanglement entropy loses meaning as an entanglement measure. Although the presence of decoherence in the unitary circuit without measurements results in area law negativity as expected from Page's theorem, we find numerically that the addition of measurements can stabilize a phase with power law scaling of negativity. This new measurement-induced phase can be understood analytically within an effective statistical mechanics model, where the power law negativity arises as the free energy cost of the measurement-induced finite temperature fluctuations of domain walls. Our work provides insight on the ability to maintain large-scale quantum coherence in nontrivial open quantum systems, an important ingredient for quantum computation.