Quantum Coding Transitions in the Presence of Boundary Dissipation*

Chaotic unitary time evolution in closed quantum systems spreads initially localized quantum information to non-local degrees of freedom. This delocalization by the intrinsic dynamics has the potential to hide information against the destructive effect of a dissipative environment giving rise to local noise. Investigating the robustness of quantum information under this complicated interplay of unitary spreading and dissipation offers a new perspective on exploring dissipative dynamical phases, while the emerging dynamical regimes have potential applications in designing quantum codes. In this work, we demonstrate a rich dynamical phase diagram in a one-dimensional quantum many-body system subject to dissipation at the boundary, displaying different regimes distinguished by the fate of quantum information at late times. Specifically, we find a phase where the information remains protected even at time scales where thermalization is typically expected, as well as a regime where all information leaks to the environment. In particular, intrinsic dynamics alone can protect a finite density of information, allowing the stable encoding of information at finite rate.