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A Concise Guide to Complex Hadamard Matrices

Wojciech Tadej

Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University, Warsaw, Poland

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and

Karol Życzkowski

Institute of Physics, Jagiellonian University, Kraków, Poland

Center for Theoretical Physics, Polish Academy of Sciences, Warsaw, Poland

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https://doi.org/10.1007/s11080-006-8220-2Cited by:181 (Source: Crossref)

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.

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