My work consists of looking at the quantum information dynamics in extended systems, often one-dimensional, in a way that is initial-state-independent (in contrast to the quenched dynamics where a system relaxes from a specific nonequilibrium state).
This question is specifically interesting in the cases where systems have conserved quantities where the study of the dynamics of quantum information relates back to the hydrodynamics of said conserved quantities.
Another portion of our group's work is done in collaboration with Dr Leek's group. Where they look at the experimental signatures of Many-Body Quantum Chaos in their superconducting qubit (transmon) based quantum simulators.