Separable Entanglement Transitions Using the Stochastic Control of Chaos

Abstract

Measurement-induced phase transitions have become an increasingly popular means of studying the dynamics of quantum trajectories. The characterization of these phase transitions often defines properties of the quantum state, such as whether the state can retain quantum information or if the state is ordered. To this extent, the dynamics of a quantum analog to the Bernoulli map can be coupled with a stochastic control protocol to yield these phase transitions. Interestingly, if the dynamics and stochastic control are implemented using single qubit measurements and Clifford gates, then two phase transitions occur at different rates of controlling the system. The two types of phase transitions indicate a change in the entanglement spread in the system and a change in the ordering in the system and have separate universalities. In contrast, without the restriction of the Clifford gates, these phase transitions would occur simultaneously, but would be dominated by the control transition's universality