Modeling Quantum Optical Components, Pulses and Fiber Channels Using OMNeT++

Quantum Key Distribution (QKD) is an innovative technology which exploits the laws of quantum mechanics to generate and distribute unconditionally secure cryptographic keys. While QKD offers the promise of unconditionally secure key distribution, real world systems are built from non-ideal components which necessitates the need to model and understand the impact these non-idealities have on system performance and security. OMNeT++ has been used as a basis to develop a simulation framework to support this endeavor. This framework, referred to as "qkdX" extends OMNeT++'s module and message abstractions to efficiently model optical components, optical pulses, operating protocols and processes. This paper presents the design of this framework including how OMNeT++'s abstractions have been utilized to model quantum optical components, optical pulses, fiber and free space channels. Furthermore, from our toolbox of created components, we present various notional and real QKD systems, which have been studied and analyzed.Comment: Published in: A. F\"orster, C. Minkenberg, G. R. Herrera, M. Kirsche (Eds.), Proc. of the 2nd OMNeT++ Community Summit, IBM Research - Zurich, Switzerland, September 3-4, 201

The Influence of Diffusion on Surface Reaction Kinetics

An analysis is given of diffusion-influenced surface reactions using models similar to those used in solution kinetics. It is shown that a pure two-dimensional model of surface reactions yields no steady state rate constant. By incorporation of adsorption and desorption processes the deficiencies in the two-dimensional results are eliminated. Expressions are derived for diffusion-controlled and diffusion-influenced rate constants for surface reactions. Expressions are also derived for the activation energies of these surface reactions. It is shown that the activation energy for diffusion-controlled reactions wiII approximately be given by the activation energy for surface diffusion. Bounding expressions are developed for the activation energy for diffusion-influenced reactions. Comparisons are made betweeen Langmuir-Hinshe1wood and Eley-Rideal mechanisms, and it is found that Langmuir-Hinshelwood mechanisms should be more important than Eley-Rideal processes for many surface reactions

Modeling, Simulation, and Performance Analysis of Decoy State Enabled Quantum Key Distribution Systems

Quantum Key Distribution (QKD) systems exploit the laws of quantum mechanics to generate secure keying material for cryptographic purposes. To date, several commercially viable decoy state enabled QKD systems have been successfully demonstrated and show promise for high-security applications such as banking, government, and military environments. In this work, a detailed performance analysis of decoy state enabled QKD systems is conducted through model and simulation of several common decoy state configurations. The results of this study uniquely demonstrate that the decoy state protocol can ensure Photon Number Splitting (PNS) attacks are detected with high confidence, while maximizing the system’s quantum throughput at no additional cost. Additionally, implementation security guidance is provided for QKD system developers and users

Optimizing Decoy State Enabled Quantum Key Distribution Systems to Maximize Quantum Throughput and Detect Photon Number Splitting Attacks with High Confidence

Quantum Key Distribution (QKD) is an innovative quantum communications protocol which exploits the laws of quantum mechanics to generate unconditionally secure cryptographic keying material between two geographically separated parties. The unique nature of QKD shows promise for high-security applications such as those found in banking, government, and military environments. However, QKD systems contain implementation non-idealities which can negatively impact their performance and security.In particular, QKD systems often employ the decoy state protocol to improve system throughput and mitigate the threat of Photon Number Splitting (PNS) attacks. In this work, a detailed analysis of the decoy state protocol is conducted which optimizes both performance in terms of quantum throughput and security with respect to detecting PNS attacks. The results of this study uniquely demonstrate that the decoy state protocol can ensure PNS attacks are detected with high confidence, while maximizing the secure key generation rate at no additional cost. Additionally, implementation security guidance is provided for QKD system developers and users

Value at Risk models with long memory features and their economic performance

We study alternative dynamics for Value at Risk (VaR) that incorporate a slow moving component and information on recent aggregate returns in established quantile (auto) regression models. These models are compared on their economic performance, and also on metrics of first-order importance such as violation ratios. By better economic performance, we mean that changes in the VaR forecasts should have a lower variance to reduce transaction costs and should lead to lower exceedance sizes without raising the average level of the VaR. We find that, in combination with a targeted estimation strategy, our proposed models lead to improved performance in both statistical and economic terms

Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model

A dual formulation of group field theories, obtained by a Fourier transform mapping functions on a group to functions on its Lie algebra, has been proposed recently. In the case of the Ooguri model for SO(4) BF theory, the variables of the dual field variables are thus so(4) bivectors, which have a direct interpretation as the discrete B variables. Here we study a modification of the model by means of a constraint operator implementing the simplicity of the bivectors, in such a way that projected fields describe metric tetrahedra. This involves a extension of the usual GFT framework, where boundary operators are labelled by projected spin network states. By construction, the Feynman amplitudes are simplicial path integrals for constrained BF theory. We show that the spin foam formulation of these amplitudes corresponds to a variant of the Barrett-Crane model for quantum gravity. We then re-examin the arguments against the Barrett-Crane model(s), in light of our construction.Comment: revtex, 24 page

Colored Group Field Theory

Group field theories are higher dimensional generalizations of matrix models. Their Feynman graphs are fat and in addition to vertices, edges and faces, they also contain higher dimensional cells, called bubbles. In this paper, we propose a new, fermionic Group Field Theory, posessing a color symmetry, and take the first steps in a systematic study of the topological properties of its graphs. Unlike its bosonic counterpart, the bubbles of the Feynman graphs of this theory are well defined and readily identified. We prove that this graphs are combinatorial cellular complexes. We define and study the cellular homology of this graphs. Furthermore we define a homotopy transformation appropriate to this graphs. Finally, the amplitude of the Feynman graphs is shown to be related to the fundamental group of the cellular complex

Bubbles and jackets: new scaling bounds in topological group field theories

We use a reformulation of topological group field theories in 3 and 4 dimensions in terms of variables associated to vertices, in 3d, and edges, in 4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4 dimensions, we obtain a bubble bound proving the suppression of singular topologies with respect to the first terms in the perturbative expansion (in the cut-off). We also prove a new, stronger jacket bound than the one currently available in the literature. We expect these results to be relevant for other tensorial field theories of this type, as well as for group field theory models for 4d quantum gravity.Comment: v2: Minor modifications to match published versio

Encoding simplicial quantum geometry in group field theories

We show that a new symmetry requirement on the GFT field, in the context of an extended GFT formalism, involving both Lie algebra and group elements, leads, in 3d, to Feynman amplitudes with a simplicial path integral form based on the Regge action, to a proper relation between the discrete connection and the triad vectors appearing in it, and to a much more satisfactory and transparent encoding of simplicial geometry already at the level of the GFT action.Comment: 15 pages, 2 figures, RevTeX, references adde

Topological Graph Polynomials in Colored Group Field Theory

In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph \cG_{\partial} of an open graph \cG and prove it is a cellular complex. Using this structure we generalize the topological (Bollobas-Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension