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Entropy
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Random Matrix Approaches in Classical and Quantum Information Theory
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Random Matrix Approaches in Classical and Quantum Information Theory

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (30 June 2020) | Viewed by 5354

Special Issue Editors

Dr. Lu Wei

E-Mail Website
Guest Editor
Department of Electrical and Computer Engineering, University of Michigan-Dearborn, Dearborn, MI 48128, USA
Interests: coding theory; computer algebra system; information theory (classical and quantum); orthogonal polynomials; random matrix theory; special functions
Special Issues, Collections and Topics in MDPI journals
Dr. Antonia Tulino

E-Mail Website
Guest Editor
1. Univerisità Federico II, Napoli, Italy
2. Bell Labs, NJ 07974-0636, USA
Dr. Santosh Kumar

E-Mail Website
Guest Editor
Department of Physics, Shiv Nadar University, Uttar Pradesh 201314, India

Special Issue Information

Dear Colleagues,

Classical information theory is the theory behind modern development of computing, communication, data compression, and other fields. As its classical counterpart, quantum information theory aims at understanding the theoretical underpinnings of quantum sciences that will enable future quantum technologies. Random matrix theory, originating from physics, emerges as an indispensable tool in understanding various problems in both classical and quantum information theory.

This Special Issue solicits recent advances in random matrix methods to classical and quantum information theory. Topics include but are not limited to applications of random matrix theory to:

  • Caching and data retrieval
  • Coding theory (classical and quantum)
  • Communications theory (classical and quantum)
  • Compressed sensing
  • Concentration of measure techniques
  • Deep neural networks
  • Detection and estimation
  • Geometry of quantum states
  • Graph signal processing
  • Quantum chaos and entanglement
  • Random density matrices and entropies
  • Spectral methods for graph clustering and classification

Dr. Lu Wei
Dr. Antonia Tulino
Dr. Santosh Kumar
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Research

36 pages, 2612 KiB  
Article
On Products of Random Matrices
by Natalia Amburg, Aleksander Orlov and Dmitry Vasiliev
Entropy 2020, 22(9), 972; https://doi.org/10.3390/e22090972 - 31 Aug 2020
Cited by 8 | Viewed by 2410
Abstract
We introduce a family of models, which we name matrix models associated with children’s drawings—the so-called dessin d’enfant. Dessins d’enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky). The vertices of such a graph are [...] Read more.
We introduce a family of models, which we name matrix models associated with children’s drawings—the so-called dessin d’enfant. Dessins d’enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky). The vertices of such a graph are small disks that we call stars. We attach random matrices to the edges of the graph and get multimatrix models. Additionally, to the stars we attach source matrices. They play the role of free parameters or model coupling constants. The answers for our integrals are expressed through quantities that we call the “spectrum of stars”. The answers may also include some combinatorial numbers, such as Hurwitz numbers or characters from group representation theory. Full article
(This article belongs to the Special Issue Random Matrix Approaches in Classical and Quantum Information Theory)
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18 pages, 364 KiB  
Article
Matrix Integral Approach to MIMO Mutual Information Statistics in High-SNR Regime
by Lu Wei, Chun-Hung Liu, Ying-Chang Liang and Zhidong Bai
Entropy 2019, 21(11), 1071; https://0-doi-org.brum.beds.ac.uk/10.3390/e21111071 - 01 Nov 2019
Cited by 3 | Viewed by 2390
Abstract
In this work, an analytical framework for deriving the exact moments of multiple-input- multiple-output (MIMO) mutual information in the high-signal-to-noise ratio (SNR) regime is proposed. The idea is to make efficient use of the matrix-variate densities of channel matrices instead of the eigenvalue [...] Read more.
In this work, an analytical framework for deriving the exact moments of multiple-input- multiple-output (MIMO) mutual information in the high-signal-to-noise ratio (SNR) regime is proposed. The idea is to make efficient use of the matrix-variate densities of channel matrices instead of the eigenvalue densities as in the literature. The framework is applied to the study of the emerging models of MIMO Rayleigh product channels and Jacobi MIMO channels, which include several well-known channels models as special cases. The corresponding exact moments of any order for the high-SNR mutual information are derived. The explicit moment expressions are utilized to construct simple yet accurate approximations to the outage probability. Despite the high-SNR nature, simulation shows usefulness of the approximations with finite SNR values in the scenario of low outage probability relevant to MIMO communications. Full article
(This article belongs to the Special Issue Random Matrix Approaches in Classical and Quantum Information Theory)
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