Asymmetries in symmetric quantum walks on two-dimensional networks

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast, directed transport through the network to the opposite corner. This transport is not ballistic in nature, but rather produced by quantum mechanical interference. In the long time limit, certain walks show an asymmetric limiting probability distribution; this feature depends on the starting site and, remarkably, on the precise size of the network. The limiting probability distributions show patterns which are correlated with the initial condition. This might have consequences for the application of continuous time quantum walk algorithms.Comment: 9 pages, 12 figures, revtex

Quantum Entanglement Percolation

Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes evolution of network connectivity with respect to some network parameters. In this framework, the probability to establish perfect entanglement between two remote partners decays exponentially with the distance between them before the percolation transition point, which unambiguously defines percolation properties of any classical network or lattice. Here we introduce quantum networks created with local operations and classical communication, which exhibit non-classical percolation transition points leading to the striking communication advantages over those offered by the corresponding classical networks. We show, in particular, how to establish perfect entanglement between any two nodes in the simplest possible network -- the 1D chain -- using imperfect entangled pairs of qubits.Comment: 5 pages, 2 figure

Quantum Computing Assisted Medium Access Control for Multiple Client Station Networks

A medium access control protocol based on quantum entanglement has been introduced by Berces and Imre (2006) and Van Meter (2012). This protocol entirely avoids collisions. It is assumed that the network consists of one access point and two client stations. We extend this scheme to a network with an arbitrary number of client stations. We propose three approaches, namely, the qubit distribution, transmit first election and temporal ordering protocols. The qubit distribution protocol leverages the concepts of Bell-EPR pair or W state triad. It works for networks of up to four CSs. With up to three CSs, there is no probability of collision. In a four-CS network, there is a low probability of collision. The transmit first election protocol and temporal ordering protocols work for a network with any number of CSs. The transmit first election builds upon the concept of W state of size corresponding to the number of client stations. It is fair and collision free. The temporal ordering protocol employs the concepts of Lehmer code and quantum oracle. It is collision free, has a normalized throughput of 100% and achieves quasi-fairness.Comment: 18 pages, 12 figures, 3 tables; manuscript under revie