On the Geometric Measures of Entanglement

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three qubit case is discussed and argued that the distance to the W states is a new monotone.Comment: 7 pages, 1 figures, minor content change, references added, 1 figure adde

Auguries by Clea Roberts

Review of Clea Roberts\u27 Auguries

Uplink Performance Analysis in D2D-Enabled mmWave Cellular Networks

In this paper, we provide an analytical framework to analyze the uplink performance of device-to-device (D2D)-enabled millimeter wave (mmWave) cellular networks. Signal-to- interference-plus-noise ratio (SINR) outage probabilities are derived for both cellular and D2D links using tools from stochastic geometry. The distinguishing features of mmWave communications such as directional beamforming and having different path loss laws for line-of-sight (LOS) and non-line-of-sight (NLOS) links are incorporated into the outage analysis by employing a flexible mode selection scheme and Nakagami fading. Also, the effect of beamforming alignment errors on the outage probability is investigated to get insight on the performance in practical scenarios.Comment: arXiv admin note: text overlap with arXiv:1510.05961, arXiv:1608.0179

Average Error Probability Analysis in mmWave Cellular Networks

In this paper, a mathematical framework for the analysis of average symbol error probability (ASEP) in millimeter wave (mmWave) cellular networks with Poisson Point Process (PPP) distributed base stations (BSs) is developed using tools from stochastic geometry. The distinguishing features of mmWave communications such as directional beamforming and having different path loss laws for line-of-sight (LOS) and non-line-of-sight (NLOS) links are incorporated in the average error probability analysis. First, average pairwise error probability (APEP) expression is obtained by averaging pairwise error probability (PEP) over fading and random shortest distance from mobile user (MU) to its serving BS. Subsequently, average symbol error probability is approximated from APEP using the nearest neighbor (NN) approximation. ASEP is analyzed for different antenna gains and base station densities. Finally, the effect of beamforming alignment errors on ASEP is investigated to get insight on more realistic cases.Comment: Presented at IEEE VTC2015-Fal

Interaction of Relativistic Bosons with Localized Sources on Riemannian Surfaces

We study the interaction of mutually non-interacting Klein-Gordon particles with localized sources on stochastically complete Riemannian surfaces. This asymptotically free theory requires regularization and coupling constant renormalization. Renormalization is performed non-perturbatively using the orthofermion algebra technique and the principal operator $\Phi$ is found. The principal operator is then used to obtain the bound state spectrum, in terms of binding energies to single Dirac-delta function centers. The heat kernel method allows us to generalize this procedure to compact and Cartan-Hadamard type Riemannian manifolds. We make use of upper and lower bounds on the heat kernel to constrain the ground state energy from below thus confirming that our neglect of pair creation is justified for certain ranges of parameters in the problem.Comment: 29 page