Speaker: Haining Pan (Rutgers University) Title: When can a classical control-induced phase transition herald the measurement-induced phase transition? Abstract: The experimental observation in the measurement-induced phase transition from the volume-law entangled state to the area-law entangled state is challenging due to post-selection issues where the ensemble-averaged density matrix always flows to the infinite-temperature Gibbs state. One clever way to avoid it is to steer the dynamics onto a controlled phase with predetermined fixed points to herald the entanglement transition via the control transition. However, it remains uncertain whether these two transitions always coincide. In this work, we study the topology of the phase diagram of a family of quantum models inspired by the classical Bernoulli map under stochastic control. The quantum models inherit a control-induced phase transition from the classical model and also manifest an entanglement phase transition intrinsic to the quantum setting. This measurement-induced phase transition has been shown in various settings to either coincide or split off from the control transition, but a systematic understanding of the necessary and sufficient conditions for the two transitions to coincide has so far been lacking. We generalize the control map to allow for either local or global control action. While this does not affect the classical aspects of the control transition, it significantly influences the quantum dynamics, leading to a locality-dependent quantum criticality. In the presence of a global control map, the two transitions coincide and the control-induced phase transition dominates the measurement-induced phase transition. Contrarily, the two transitions split in the presence of the local control map or additional projective measurements and generically take on distinct universality classes. For local control, the measurement-induced phase transition recovers the Haar logarithmic conformal field theory universality class found in other such transition. However, for global control, a novel universality class with correlation length exponent $ u \approx 0.7$ emerges from the interplay of control and projective measurements. Throughout, the control-induced phase transition displays critical features described by a random walk. This work provides a more refined understanding of the relationship between the control- and measurement-induced phase transitions.