TL;DR
This paper introduces an analytical approach to generate complex Hadamard matrices using mutually unbiased bases and a nonlinear doubling formula, exemplified by a new family in eight dimensions.
Contribution
It presents a novel analytical method for constructing complex Hadamard matrices from mutually unbiased bases and a nonlinear doubling formula, expanding the known families.
Findings
Generated a new family of eight-dimensional Hadamard matrices
Method depends on five arbitrary parameters with unit modulus
Demonstrated the method with the n=4 case
Abstract
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.
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