Hadamard Matrices from Mutually Unbiased Bases

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.

References in corpus (6)

• A new proof for the existence of mutually unbiased bases
• Mubs and Hadamards of Order Six
• Constructions of Mutually Unbiased Bases
• Exotic complex Hadamard matrices, and their equivalence
• Separation of unistochastic matrices from the double stochastic ones. Recovery of a 3 x 3 unitary matrix from experimental data
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Cited by in corpus (5)

• On mutually unbiased bases
• Isolated Hadamard Matrices from Mutually Unbiased Product Bases
• A new method to construct families of complex Hadamard matrices in even dimensions
• On quaternary complex Hadamard matrices of small orders
• Equivalence of Complex Hadamard Matrices