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

Abstract

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.

17 pages; Contribution to the workshop "Quantum Physics in higher dimensional Hilbert Spaces", Traunkirchen, Austria, July 2010

Cited by in corpus (12)

• Universal Linear Optics
• Self-testing mutually unbiased bases in the prepare-and-measure scenario
• Isolated Hadamard Matrices from Mutually Unbiased Product Bases
• On properties of Karlsson Hadamards and sets of Mutually Unbiased Bases in dimension six
• $BCCB$ complex Hadamard matrices of order 9, and MUBs
• Temperley-Lieb R-matrices from generalized Hadamard matrices
• Theory of homotopes in application to mutually unbiased bases, harmonic analysis on graphs and perverse sheaves
• Block-Circulant Complex Hadamard Matrices
• Finite-Function-Encoding Quantum States
• A characterization of complex Hadamard matrices appearing in families of MUB triplets
• Mutually unbiased bases containing a complex Hadamard matrix of Schmidt rank three
• Equivalence of Complex Hadamard Matrices