Complex Hadamard matrices of order 6: a four-parameter family

Details Complex Hadamard matrices of order 6: a four-parameter family Complex Hadamard matrices of order 6: a four-parameter family

2010-08-03

arxiv.org/abs/1008.0632v1

Mathematics

Operator Algebras

17 pages; Contribution to the workshop "Quantum Physics in higher dimensional Hilbert Spaces", Traunkirchen, Austria, July 201

Scientific paper

In this paper we construct a new, previously unknown four-parameter family of complex Hadamard matrices of order 6, the entries of which are described by algebraic functions of roots of various sextic polynomials. We conjecture that the new, generic family G together with Karlsson's degenerate family K and Tao's spectral matrix S form an exhaustive list of complex Hadamard matrices of order 6. Such a complete characterization might finally lead to the solution of the famous MUB-6 problem.

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