Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction

A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in the Shannon theoretic sense and that are decodable in polynomial time are presented. The rate is the highest among those known to be achievable by CSS codes. Moreover, the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range.Comment: 16 pages, 3 figures. Ver.4: Title changed. Ver.3: Due to a request of the AE of the journal, the present version has become a combination of (thoroughly revised) quant-ph/0610194 and the former quant-ph/0610195. Problem formulations of polynomial complexity are strictly followed. An erroneous instance of a lower bound on minimum distance was remove

Tools for calculations in color space

Both the higher energy and the initial state colored partons contribute to making exact calculations in QCD color space more important at the LHC than at its predecessors. This is applicable whether the method of assessing QCD is fixed order calculation, resummation, or parton showers. In this talk we discuss tools for tackling the problem of performing exact color summed calculations. We start with theoretical tools in the form of the (standard) trace bases and the orthogonal multiplet bases (for which a general method of construction was recently presented). Following this, we focus on two new packages for performing color structure calculations: one easy to use Mathematica package, ColorMath, and one C++ package, ColorFull, which is suitable for more demanding calculations, and for interfacing with event generators.Comment: 7 pages, to appear in the proceedings of the XXI International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2013), 22-26 April 2013, Marseilles, Franc

Model Checking Social Network Models

A social network service is a platform to build social relations among people sharing similar interests and activities. The underlying structure of a social networks service is the social graph, where nodes represent users and the arcs represent the users' social links and other kind of connections. One important concern in social networks is privacy: what others are (not) allowed to know about us. The "logic of knowledge" (epistemic logic) is thus a good formalism to define, and reason about, privacy policies. In this paper we consider the problem of verifying knowledge properties over social network models (SNMs), that is social graphs enriched with knowledge bases containing the information that the users know. More concretely, our contributions are: i) We prove that the model checking problem for epistemic properties over SNMs is decidable; ii) We prove that a number of properties of knowledge that are sound w.r.t. Kripke models are also sound w.r.t. SNMs; iii) We give a satisfaction-preserving encoding of SNMs into canonical Kripke models, and we also characterise which Kripke models may be translated into SNMs; iv) We show that, for SNMs, the model checking problem is cheaper than the one based on standard Kripke models. Finally, we have developed a proof-of-concept implementation of the model-checking algorithm for SNMs.Comment: In Proceedings GandALF 2017, arXiv:1709.0176