Role models for complex networks

We present a framework for automatically decomposing ("block-modeling") the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph ("block model") depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both two-mode and one-mode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy

Non-locality and Communication Complexity

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the information counterpart of computing. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. We review the area of quantum communication complexity, and show how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on non-locality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics, and could even yield new proposals for experiments that test the foundations of physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in Reviews of Modern Physic

Interference effects in the Coulomb blockade regime: current blocking and spin preparation in symmetric nanojunctions

We consider nanojunctions in the single-electron tunnelling regime which, due to a high degree of spatial symmetry, have a degenerate many body spectrum. As a consequence, interference phenomena which cause a current blocking can occur at specific values of the bias and gate voltage. We present here a general formalism to give necessary and sufficient conditions for interference blockade also in the presence of spin polarized leads. As an example we analyze a triple quantum dot single electron transistor (SET). For a set-up with parallel polarized leads, we show how to selectively prepare the system in each of the three states of an excited spin triplet without application of any external magnetic field.Comment: 10 pages, 9 figures. Corrected typos and updated reference

Voltage-driven quantum oscillations in graphene

We predict unusual (for non-relativistic quantum mechanics) electron states in graphene, which are localized within a finite-width potential barrier. The density of localized states in the sufficiently high and/or wide graphene barrier exhibits a number of singularities at certain values of the energy. Such singularities provide quantum oscillations of both the transport (e.g., conductivity) and thermodynamic properties of graphene - when increasing the barrier height and/or width, similarly to the well-known Shubnikov-de-Haas (SdH) oscillations of conductivity in pure metals. However, here the SdH-like oscillations are driven by an electric field instead of the usual magnetically-driven SdH-oscillations.Comment: 4 pages, 4 figure