Spacetime duality between localization transitions and measurement-induced transitions

Understand

Time evolution of quantum many-body systems typically leads to a state with maximal entanglement allowed by symmetries.

• Two distinct routes to impede entanglement growth are inducing localization via spatial disorder, or subjecting the system to non-unitary evolution, e.g., via projective measurements.
• Here we employ the idea of space-time rotation of a circuit to explore the relation between systems that fall into these two classes.
• In particular, by space-time rotating unitary Floquet circuits that display a localization transition, we construct non-unitary circuits that display a rich variety of entanglement scaling and phase transitions.