Hadamard matrices from mutually unbiased bases

An analytical method for getting new complex Hadamard matrices by using mutually unbiased bases and a nonlinear doubling formula is provided. The method is illustrated with the n=4 case that leads to a rich family of eight-dimensional Hadamard matrices that depend on five arbitrary parameters whose modulus is equal to unity. (C) 2010 American Institute of Physics. [doi:10.1063/1.3456082]