Entanglement phases of monitored circuits via spacetime duality*

Quantum systems subject to monitoring by an outside observer have been shown to exhibit interesting entanglement phases in their quantum trajectories, giving a new paradigm for phase structure out of equilibrium. However, observing these phases is quite challenging, as it requires tracking one out of exponentially many quantum trajectories. I will discuss how key aspects of these measurement-induced phases (including the emergence of a dynamically-generated quantum error correcting code that supports the entangling phase) are present in unitary circuits without any monitoring, and are accessible via the idea of "spacetime duality", i.e. by exchanging the roles of space and time in the dynamics. This opens the door to practical laboratory realizations and also enables the derivation of new monitored phases with "fractal" scaling of entanglement, not generically found in many-body unitary dynamics.