Constructions of complex hadamard matrices via tiling abelian groups

Máté Matolcsi, Júlia Réffy, Ferenc Szöllösi

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling of Abelian groups and constructions of complex Hadamard matrices. First, we recover a recent, very general construction of complex Hadamard matrices due to Dita [2] via a natural tiling construction. Then we find some necessary conditions for any given complex Hadamard matrix to be equivalent to a Dita-type matrix. Finally, using another tiling construction, due to Szabó [8], we arrive at new parametric families of complex Hadamard matrices of order 8, 12 and 16, and we use our necessary conditions to prove that these families do not arise with Dita's construction. These new families complement the recent catalogue [10] of complex Hadamard matrices of small order.

Original languageEnglish
Pages (from-to)247-263
Number of pages17
JournalOpen Systems and Information Dynamics
Volume14
Issue number3
DOIs
Publication statusPublished - Sep 2007

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Hadamard matrices
Hadamard Matrix
Tiling
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matrices
Quantum Information Theory
Necessary Conditions
information theory
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ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematical Physics
  • Information Systems
  • Statistical and Nonlinear Physics
  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physical and Theoretical Chemistry

Cite this

Constructions of complex hadamard matrices via tiling abelian groups. / Matolcsi, Máté; Réffy, Júlia; Szöllösi, Ferenc.

In: Open Systems and Information Dynamics, Vol. 14, No. 3, 09.2007, p. 247-263.

Research output: Contribution to journalArticle

Matolcsi, Máté ; Réffy, Júlia ; Szöllösi, Ferenc. / Constructions of complex hadamard matrices via tiling abelian groups. In: Open Systems and Information Dynamics. 2007 ; Vol. 14, No. 3. pp. 247-263.
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