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We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
These lecture notes survey some joint work with Samson Abramsky. Somewhat informally I will discuss the main results in a pedestrian not too technical way. These include: (1) `The logic of entanglement', that is, the identification and…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and…
Quantum walks of correlated particles offer the possibility to study large-scale quantum interference, simulate biological, chemical and physical systems, and a route to universal quantum computation. Here we demonstrate quantum walks of…
Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information…
Ultracold atoms confined by engineered magnetic or optical potentials are ideal systems for studying phenomena otherwise difficult to realize or probe in the solid state because their atomic interaction strength, number of species, density,…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans…
We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies…
A framework integrating information theory and network science is proposed, giving rise to a potentially new area. By incorporating and integrating concepts such as complexity, coding, topological projections and network dynamics, the…
We study transport within a spatially heterogeneous one-dimensional quantum walk with a combination of hierarchical and random barriers. Recent renormalization group calculations for a spatially disordered quantum walk with a regular…
We propose a measure to quantify the efficiency of classical and quantum mechanical transport processes on graphs. The measure only depends on the density of states (DOS), which contains all the necessary information about the graph. For…
Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e.…
Tap-proof long-distance quantum communication requires a deep understanding of the strong losses in transmission channels. Here we provide a rigorous treatment of the effects of beam wandering, one of the leading disturbances in atmospheric…
We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an…
The staggered quantum walk is a type of discrete-time quantum walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered…
The article deals with one- and two-particle quantum walks on a graph with Braess-like topology and analyzes the issue of network congestion in the quantum world. Our approach to the study of congestion in quantum networks is based on the…
We study entanglement distribution in quantum complex networks where nodes are connected by bipartite entangled states. These networks are characterized by a complex structure, which dramatically affects how information is transmitted…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…