Inhomogeneous substructures hidden in random networks

We study the structure of the load-based spanning tree (LST) that carries the maximum weight of the Erdos-Renyi (ER) random network. The weight of an edge is given by the edge-betweenness centrality, the effective number of shortest paths through the edge. We find that the LSTs present very inhomogeneous structures in contrast to the homogeneous structures of the original networks. Moreover, it turns out that the structure of the LST changes dramatically as the edge density of an ER network increases, from scale free with a cutoff, scale free, to a starlike topology. These would not be possible if the weights are randomly distributed, which implies that topology of the shortest path is correlated in spite of the homogeneous topology of the random network.Comment: 4 pages, 4 figure

Entangled coherent states versus entangled photon pairs for practical quantum information processing

We compare effects of decoherence and detection inefficiency on entangled coherent states (ECSs) and entangled photon pairs (EPPs), both of which are known to be particularly useful for quantum information processing (QIP). When decoherence effects caused by photon losses are heavy, the ECSs outperform the EPPs as quantum channels for teleportation both in fidelities and in success probabilities. On the other hand, when inefficient detectors are used, the teleportation scheme using the ECSs suffers undetected errors that result in the degradation of fidelity, while this is not the case for the teleportation scheme using the EPPs. Our study reveals the merits and demerits of the two types of entangled states in realizing practical QIP under realistic conditions.Comment: 9 pages, 6 figures, substantially revised version, to be published in Phys. Rev.

Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits

We propose a scheme to realize deterministic quantum teleportation using linear optics and hybrid qubits. It enables one to efficiently perform teleportation and universal linear-optical gate operations in a simple and near-deterministic manner using all-optical hybrid entanglement as off-line resources. Our analysis shows that our new approach can outperforms major previous ones when considering both the resource requirements and fault tolerance limits.Comment: 10 pages, 5 figures; extended version, title, abstract and figures changed, details added, to be published in Phys. Rev.

Scale-free trees: the skeletons of complex networks

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights are given by the edge betweenness centralities. We find that a scale-free tree and shortcuts organize a complex network. The spanning tree shows robust betweenness centrality distribution that was observed in scale-free tree models. It turns out that the shortcut distribution characterizes the properties of original network, such as the clustering coefficient and the classification of networks by the betweenness centrality distribution

Importance sampling schemes for evidence approximation in mixture models

The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete exploration by a simulated Markov chain (e.g., a Gibbs sequence) of the collection of posterior modes, a phenomenon also known as lack of label switching, as all possible label permutations must be simulated by a chain in order to converge and hence overcome the bias. In an importance sampling approach, imposing label switching to the importance function results in an exponential increase of the computational cost with the number of components. In this paper, two importance sampling schemes are proposed through choices for the importance function; a MLE proposal and a Rao-Blackwellised importance function. The second scheme is called dual importance sampling. We demonstrate that this dual importance sampling is a valid estimator of the evidence and moreover show that the statistical efficiency of estimates increases. To reduce the induced high demand in computation, the original importance function is approximated but a suitable approximation can produce an estimate with the same precision and with reduced computational workload.Comment: 24 pages, 5 figure

Bifurcations and bistability in cavity assisted photoassociation of Bose-Einstein condensed molecules

We study the photo-association of Bose-Einstein condensed atoms into molecules using an optical cavity field. The driven cavity field introduces a new dynamical degree of freedom into the photoassociation process, whose role in determining the stationary behavior has not previously been considered. The semiclassical stationary solutions for the atom and molecules as well as the intracavity field are found and their stability and scaling properties are determined in terms of experimentally controllable parameters including driving amplitude of the cavity and the nonlinear interactions between atoms and molecules. For weak cavity driving, we find a bifurcation in the atom and molecule number occurs that signals a transition from a stable steady state to nonlinear Rabi oscillations. For a strongly driven cavity, there exists bistability in the atom and molecule number

Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals

The quasi-unit cell picture describes the atomic structure of quasicrystals in terms of a single, repeating cluster which overlaps neighbors according to specific overlap rules. In this paper, we discuss the precise relationship between a general atomic decoration in the quasi-unit cell picture atomic decorations in the Penrose tiling and in related tiling pictures. Using these relations, we obtain a simple, practical method for determining the density, stoichiometry and symmetry of a quasicrystal based on the atomic decoration of the quasi-unit cell taking proper account of the sharing of atoms between clusters.Comment: 14 pages, 8 figure

Fundamental Structural Constraint of Random Scale-Free Networks

We study the structural constraint of random scale-free networks that determines possible combinations of the degree exponent $\gamma$ and the upper cutoff $k_c$ in the thermodynamic limit. We employ the framework of graphicality transitions proposed by [Del Genio and co-workers, Phys. Rev. Lett. {\bf 107}, 178701 (2011)], while making it more rigorous and applicable to general values of kc. Using the graphicality criterion, we show that the upper cutoff must be lower than $k_c N^{1/\gamma}$ for $\gamma < 2$, whereas any upper cutoff is allowed for $\gamma > 2$. This result is also numerically verified by both the random and deterministic sampling of degree sequences.Comment: 5 pages, 4 figures (7 eps files), 2 tables; published versio

Conditional Production of Superpositions of Coherent States with Inefficient Photon Detection

It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude ($\alpha>2$) and high fidelity ($F>0.99$). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.Comment: Some important new results added, to appear in Phys.Rev.A (Rapid Communication