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arxiv: quant-ph/0512154 · v2 · submitted 2005-12-19 · 🪐 quant-ph · math.CO· math.RA

A concise guide to complex Hadamard matrices

classification 🪐 quant-ph math.COmath.RA
keywords complexhadamardmatricesarbitrarybasiccasescatalogueconcise
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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 dimension 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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17

    math.CO 2026-05 unverdicted novelty 6.0

    Two explicit quantum Latin squares of order 6 are constructed with cardinalities 13 and 17 using direct-sum decompositions and Hadamard pairs.

  2. Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17

    math.CO 2026-05 unverdicted novelty 6.0

    Explicit constructions of three quantum Latin squares of order 6 achieving cardinalities 13, 15, and 17 via orthogonal decompositions and Hadamard pairs.