Complex Hadamard matrices of order 6: a four-parameter family
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In this paper, we construct a new, previously unknown four-parameter family of complex Hadamard matrices of order 6, the entries of which are described by algebraic functions of roots of various sextic polynomials. We conjecture that the new, generic family G6(4) together with Karlsson's degenerate family K6(3) and Tao's spectral matrix S(0)6 form an exhaustive list of complex Hadamard matrices of order 6. Such a complete characterization might finally lead to the solution of the problem of mutually unbiased bases in ℂ6.
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In LO experimental implementations, discrimination among CHMs can be accomplished via the observation of characteristic patterns of photonic quantum interference.
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- Authors
- Szöllősi, F.
- Affiliations
- Central European University (AT)
- Corresponding author
- Szöllősi, Ferenc
- Venue
- Journal of the London Mathematical Society
- Publisher
- Wiley
- Published
- 2012-03-09
- Volume
- 85
- Issue
- 3
- Pages
- 616-632
- ISSN
- 0024-6107 (ISSN-L)
- OpenAlex
- W2123862442
- Cited by
- 30
- References
- 0
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 2 · 2023: 1 · 2022: 2 · 2021: 3 · 2020: 2 · 2019: 4 · 2018: 1 · 2017: 2 · 2016: 2 · 2015: 1 · 2014: 4 · 2013: 1 · 2012: 1
- FWCI
- 2.20
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Journal of the London Mathematical Society (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Finite Group Theory Research
- Keywords
- complex Hadamard matrices, algebraic functions, mutually unbiased bases
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