Measurement-induced entanglement and control transitions using feedback

In recent years, substantial progress has been achieved in understanding entanglement transitions in monitored quantum systems. In this talk, I will summarize some key facts we’ve learned and how they can be used in quantum control protocols. Drawing parallels with classically chaotic systems, we identify features that link and delink measurement and control transitions. In particular, by strategically engineering around an (approximate) unstable fixed point, control can be achieved at or above the measurement-induced phase transition. When these points coincide, the critical properties of control dominate other critical properties, becoming observable in linear operators in the density matrix. Conversely, when these transitions diverge, the entanglement transition can achieve different critical properties. We substantiate these findings through several versions of a quantum analog of the Bernoulli map: A purely quantum version, a stabilizer state version, and a limit that can be simulated classically as a (correlated) percolation problem. Finally, we point to some critical unanswered questions in the field.

Speaker: Justin Wilson, Louisiana State University