A Concise Guide to Complex Hadamard Matrices

Authors:
Wojciech Tadej;Karol Życzkowski
Affiliations:
Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University, Warsaw, Poland;-
Venue:
Open Systems & Information Dynamics
Year:
2006

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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.