Abstract

The dynamics of a quantum system will often lead to the rapid generation of entanglement and the loss of locally-accessible information about an initial state. The highly-entangled states that form during these dynamics, however, can be distinct from a random pure state, though measurable diagnostics of these differences are often elusive. In this talk, I will focus on progress in understanding signatures of these differences in two settings. First, I will discuss how the quantum butterfly effect can be identified in time-ordered correlations in quantum many-body systems in one spatial dimension. Second, I will discuss universal properties of a new kind of volume-law entangled phase that arises in the steady-state of monitored quantum dynamics, and how this phase acts as an emergent quantum error-correcting code. These results are obtained through toy models in which these dynamics are possible to study exactly, leading to useful heuristic pictures for entanglement manipulation in quantum many-body systems.