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A Concise Guide to Complex Hadamard Matrices
Open accessAbstract
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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“Whilst a full classification of N = 6 CHMs is unknown, it is currently conjectured that the set consists of an isolated matrix S (0) 6 which does not belong to any family [57], and a newly discovered four-parameter generic family G (4) 6 [58].”
From Universal linear optics (2015) · cites this paper as [58]
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Metadata
- 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
- 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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