skip to main content

Title: On the asymptotic distribution of block-modified random matrices

We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute the asymptotic eigenvalue distribution of the modified matrices in terms of the initial asymptotic distribution. Moreover, using recent results on operator-valued subordination, we present an algorithm that computes, numerically but in full generality, the limiting eigenvalue distribution of the modified matrices. Our analytical results cover many cases of interest in quantum information theory: we unify some known results and we obtain new distributions and various generalizations.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Probability and Statistics, CIMAT, Guanajuato (Mexico)
  2. Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany and CNRS, Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France)
  3. Department of Mathematical Structure Theory, Technische Universität Graz, Steyrergasse 30/III, 8010 Graz (Austria)
Publication Date:
OSTI Identifier:
22479620
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ASYMPTOTIC SOLUTIONS; EIGENVALUES; MATHEMATICAL SPACE; MATRICES; PROBABILITY; QUANTUM INFORMATION; RANDOMNESS; TENSORS