Nonergodic subdiffusion from Brownian motion in an inhomogeneous medium.

Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random diffusivities. The particle is never trapped but rather performs continuous Brownian motion with the local diffusion constant. Under simple assumptions on the distribution of the sizes and diffusivities, we find that the mean squared displacement displays subdiffusion due to nonergodicity for both annealed and quenched disorder. The model is formulated as a walk continuous in both time and space, similar to the Lévy walk.

Distribution of entanglement in large-scale quantum networks.

The concentration and distribution of quantum entanglement is an essential ingredient in emerging quantum information technologies. Much theoretical and experimental effort has been expended in understanding how to distribute entanglement in one-dimensional networks. However, as experimental techniques in quantum communication develop, protocols for multi-dimensional systems become essential. Here, we focus on recent theoretical developments in protocols for distributing entanglement in regular and complex networks, with particular attention to percolation theory and network-based error correction.