Cited by 263Quantum Information and CryptographyCoding theory and cryptographyQuantum Computing Algorithms and Architecture

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A Concise Guide to Complex Hadamard Matrices

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Tadej, Wojciech, Życzkowski, Karol·2006·Open Systems & Information Dynamics

DOI 10.1007/s11080-006-8220-2

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Abstract

Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for the dimensions N = 2,…,16. In particular, we explicitly write down some families of complex Hadamard matrices for N = 12, 14 and 16, which we could not find in the existing literature.

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Authors: Tadej, W., & Życzkowski, K.
Affiliations: Cardinal Stefan Wyszynski University in Warsaw (PL)
Jagiellonian University (PL)
ORCID: Życzkowski, Karol
Venue: Open Systems & Information Dynamics
Publisher: World Scientific Pub Co Pte Lt
Published: 2006-06
Volume: 13
Issue: 02
Pages: 133-177
ISSN: 1230-1612 (ISSN-L)
1793-7191
DOI: 10.1007/s11080-006-8220-2
OpenAlex: W2039842791
Cited by: 263
References: 55
Citations by year: 2026: 6 · 2025: 13 · 2024: 13 · 2023: 10 · 2022: 7 · 2021: 10 · 2020: 10 · 2019: 21 · 2018: 14 · 2017: 10 · 2016: 13 · 2015: 14 · 2014: 15 · 2013: 16 · 2012: 15
FWCI: 17.85
Type: journal article
Language: en
Open access: green
arxiv.org
Locations: Open Systems & Information Dynamics (publishedVersion)
arXiv (Cornell University) (submittedVersion)
CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
arXiv (Cornell University)
Funders: Institut Périmètre de physique théorique
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords: complex Hadamard matrices, unimodular matrices, quantum information, finite-dimensional quantum systems, matrix families

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A Concise Guide to Complex Hadamard Matrices

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