Towards a classification of 6 × 6 complex hadamard matrices

M. Matolcsi, Ferenc Szöllsi

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Complex Hadamard matrices have received considerable attention in the past few years due to their application in quantum information theory. While a complete characterization currently available [5] is only up to order 5, several new constructions of higher order matrices have appeared recently [4, 12, 2, 7, 11]. In particular, the classification of self-adjoint complex Hadamard matrices of order 6 was completed by Beuachamp and Nicoara in [2], providing a previously unknown non-affine one-parameter orbit. In this paper we classify all dephased, symmetric complex Hadamard matrices with real diagonal of order 6. Furthermore, relaxing the condition on the diagonal entries we obtain a new non-affine one-parameter orbit connecting the Fourier matrix F 6 and Di's matrix D 6. This answers a recent question of Bengtsson et al. [3].

Original languageEnglish
Pages (from-to)93-108
Number of pages16
JournalOpen Systems and Information Dynamics
Volume15
Issue number2
DOIs
Publication statusPublished - Jun 2008

Fingerprint

Hadamard matrices
Hadamard Matrix
Orbits
matrices
Connecting Orbits
Quantum Information Theory
Information theory
orbits
information theory
Orbit
Classify
entry
Higher Order
Unknown

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

Towards a classification of 6 × 6 complex hadamard matrices. / Matolcsi, M.; Szöllsi, Ferenc.

In: Open Systems and Information Dynamics, Vol. 15, No. 2, 06.2008, p. 93-108.

Research output: Contribution to journalArticle

@article{56724a2e01514045b1228fb2ccabcb0d,
title = "Towards a classification of 6 × 6 complex hadamard matrices",
abstract = "Complex Hadamard matrices have received considerable attention in the past few years due to their application in quantum information theory. While a complete characterization currently available [5] is only up to order 5, several new constructions of higher order matrices have appeared recently [4, 12, 2, 7, 11]. In particular, the classification of self-adjoint complex Hadamard matrices of order 6 was completed by Beuachamp and Nicoara in [2], providing a previously unknown non-affine one-parameter orbit. In this paper we classify all dephased, symmetric complex Hadamard matrices with real diagonal of order 6. Furthermore, relaxing the condition on the diagonal entries we obtain a new non-affine one-parameter orbit connecting the Fourier matrix F 6 and Di's matrix D 6. This answers a recent question of Bengtsson et al. [3].",
author = "M. Matolcsi and Ferenc Sz{\"o}llsi",
year = "2008",
month = "6",
doi = "10.1142/S1230161208000092",
language = "English",
volume = "15",
pages = "93--108",
journal = "Open Systems and Information Dynamics",
issn = "1230-1612",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

TY - JOUR

T1 - Towards a classification of 6 × 6 complex hadamard matrices

AU - Matolcsi, M.

AU - Szöllsi, Ferenc

PY - 2008/6

Y1 - 2008/6

N2 - Complex Hadamard matrices have received considerable attention in the past few years due to their application in quantum information theory. While a complete characterization currently available [5] is only up to order 5, several new constructions of higher order matrices have appeared recently [4, 12, 2, 7, 11]. In particular, the classification of self-adjoint complex Hadamard matrices of order 6 was completed by Beuachamp and Nicoara in [2], providing a previously unknown non-affine one-parameter orbit. In this paper we classify all dephased, symmetric complex Hadamard matrices with real diagonal of order 6. Furthermore, relaxing the condition on the diagonal entries we obtain a new non-affine one-parameter orbit connecting the Fourier matrix F 6 and Di's matrix D 6. This answers a recent question of Bengtsson et al. [3].

AB - Complex Hadamard matrices have received considerable attention in the past few years due to their application in quantum information theory. While a complete characterization currently available [5] is only up to order 5, several new constructions of higher order matrices have appeared recently [4, 12, 2, 7, 11]. In particular, the classification of self-adjoint complex Hadamard matrices of order 6 was completed by Beuachamp and Nicoara in [2], providing a previously unknown non-affine one-parameter orbit. In this paper we classify all dephased, symmetric complex Hadamard matrices with real diagonal of order 6. Furthermore, relaxing the condition on the diagonal entries we obtain a new non-affine one-parameter orbit connecting the Fourier matrix F 6 and Di's matrix D 6. This answers a recent question of Bengtsson et al. [3].

UR - http://www.scopus.com/inward/record.url?scp=69649104843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69649104843&partnerID=8YFLogxK

U2 - 10.1142/S1230161208000092

DO - 10.1142/S1230161208000092

M3 - Article

VL - 15

SP - 93

EP - 108

JO - Open Systems and Information Dynamics

JF - Open Systems and Information Dynamics

SN - 1230-1612

IS - 2

ER -