Complex Hadamard matrices for prime number

Petre Diţă

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arXiv · 1410.2134

Complex Hadamard matrices for prime number

Petre Diţă

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Abstract

In this paper we disprove the Haagerup statement that all complex Hadamard matrices of order five are equivalent with the Fourier matrix $F_5$ by constructing circulant matrices that lead to new Hadamard matrices. An important item is the construction of new mutually unbiased bases that are a basic concept of quantum theory and play an essential role in quantum tomography, quantum cryptografy, teleportation, construction of dense coding schemes, classical signal proccesing, etc.

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Petre Diţă. 2014-10-06. Complex Hadamard matrices for prime number. https://arxiv.org/abs/1410.2134

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