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A concise guide to complex Hadamard matrices. (English) Zbl 1105.15020

Summary: 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 \(N = 2,\dots, 16\). 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.
Reviewer’s addendum: Many applications of Hadamard matrices are listed. They are related to various areas: mathematics, high energy physics, quantum optics, theory of quantum information, quantum tomography.

MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
15A90 Applications of matrix theory to physics (MSC2000)
68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)
94A15 Information theory (general)
81P68 Quantum computation
81V80 Quantum optics
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References:

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