Distribution of quantum entanglement on networks
This work is part of the larger problem of preparing, between distant parties, entangled states that are consumed when performing quantum computational tasks. One begins with quantum systems occupying vertices of a graph which can be, for instance, a regular lattice, or a complex network. The entanglement is encoded in the edges of the graph. Various studies have considered initial states and subsystems that are bipartite, multipartite, pure, or mixed; but the entanglement is always local. The questions then concern manipulating the initial system (using a restricted class of operations) to entangle widely separated nodes. For instance: What is the most efficient protocol for achieving long-range entanglement ? Given a class of networks, is there a minimum entanglement below which long-range entanglement is impossible?
Anomalous transport on cell membranes
I am working in a collaboration between the groups of Maciej Lewenstein and María García-Parajo at ICFO. We study anomalous transport of transmembrane receptors in eukaryotic cells. This is part of the larger question of the origin and functional significance of subdiffusive motion of subcellular structures, which has become a major focus of research. We look for answers to questions such as: Is the subdiffusive motion due to energetic traps, or geometric traps, or both ? What are the scales of inhomogeneity in the effective matrix that the receptors see, or are there scale-free regimes ?