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arXiv:quant-ph/0512154 · Open Systems & Information Dynamics

A Concise Guide to Complex Hadamard Matrices

Wojciech Tadej, Karol Życzkowski

Published May 19, 2006• 263 citations
arXivHTMLPDF

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.

DOI
10.1007/s11080-006-8220-2

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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 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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