The competition between scrambling and projective measurements can lead to measurement-induced entanglement phase transitions (MIPT). In this work, we show that the universality class of the MIPT can be drastically altered when the system has a diffusing conserved density. As a numerical tractable model of this, we study a $1+\mathrm{1d}$ random Clifford circuit locally monitored by classically diffusing particles (“measurers”). The resulting diffusive correlations in the measurement density are a relevant perturbation to the usual space-time random MIPT critical point, producing a new universality class for this phase transition. We find “Griffiths-like” effects due to rare space-time regions where, e.g., the diffusive measurers have a low or high density, but these are considerably weaker than the Griffiths effects that occur with quenched randomness that produce rare spatial regions with infinite lifetime.

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• Phase transitions
• Quantum circuits
• Quantum entanglement
• Disordered systems