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Complex Hadamard matrices of order 6: a four-parameter family
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Complex Hadamard matrices of order 6: a four-parameter family
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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.
Forward citations
Cited by 2 Pith papers
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Quantum Latin Squares of Order Six with Cardinalities Nineteen, Twenty-One, Twenty-Three, Twenty-Five, and Twenty-Seven
Explicit order-6 quantum Latin squares exist with cardinalities 19, 21, and 23, completing all values in 6–24 except the impossible 7.
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Quantum Latin Squares of Order Six with Cardinalities Nineteen, Twenty-One, Twenty-Three, Twenty-Five, and Twenty-Seven
Explicit six-by-six quantum Latin squares with 19, 21, 23, 25, and 27 distinct states are constructed, completing the order-six cardinality list through 28.
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