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Entropy 2015, 17(5), 3376-3399; doi:10.3390/e17053376

Non-Abelian Topological Approach to Non-Locality of a Hypergraph State

1
Institute of Nuclear Sciences Vinca, P.O. Box 522, 11000 Belgrade, Serbia
2
University of Belgrade, Studentski trg 1, 11000 Belgrade, Serbia
Academic Editors: Jiannis Pachos, Demosthenes Ellinas, Giorgio Kaniadakis and Antonio M. Scarfone
Received: 16 February 2015 / Revised: 16 April 2015 / Accepted: 8 May 2015 / Published: 15 May 2015
(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)
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Abstract

We present a theoretical study of new families of stochastic complex information modules encoded in the hypergraph states which are defined by the fractional entropic descriptor. The essential connection between the Lyapunov exponents and d-regular hypergraph fractal set is elucidated. To further resolve the divergence in the complexity of classical and quantum representation of a hypergraph, we have investigated the notion of non-amenability and its relation to combinatorics of dynamical self-organization for the case of fractal system of free group on finite generators. The exact relation between notion of hypergraph non-locality and quantum encoding through system sets of specified non-Abelian fractal geometric structures is presented. Obtained results give important impetus towards designing of approximation algorithms for chip imprinted circuits in scalable quantum information systems. View Full-Text
Keywords: non-Abelian group; hypergraph state; topological system; non-locality; geometry information non-Abelian group; hypergraph state; topological system; non-locality; geometry information
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Berec, V. Non-Abelian Topological Approach to Non-Locality of a Hypergraph State. Entropy 2015, 17, 3376-3399.

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