Phys. Rev. X (in the press); preprint at https://arxiv.org/abs/1710.09835

Phys. Rev. X (in the press); preprint at https://arxiv.org/abs/1710.09827

A drop of ink gets diluted in water. The movement of the ink particles — from regions of high to low concentration — is governed by diffusion, in which mass conservation plays a crucial role. In the quantum world, the evolution of a system is constrained by unitarity in addition to conservation laws. So how does quantum information propagate under the combination of these constraints? Vedika Khemani and co-workers have addressed this problem, revealing an interplay between the conservation of an actual observable and unitarity.

Previous studies indicated that with the unitary constraint alone, quantum information propagates ballistically, leading to a light-cone structure in spacetime. Khemani et al. considered an additional charge-conservation constraint, and found that the information-spreading front still travelled ballistically. However, coupling between the unitary evolution and the diffusion induced more complicated relaxation dynamics behind the ballistic front. In a related work, Tibor Rakovszky and co-workers reached similar conclusions with a slightly different approach.