New results on the parametrisation of complex Hadamard matrices

Details New results on the parametrisation of complex Hadamard matrices New results on the parametrisation of complex Hadamard matrices

2002-12-06

arxiv.org/abs/quant-ph/0212036v2

Physics

Quantum Physics

27 pages

Scientific paper

In this paper we provide an analytical procedure which leads to a system of $(n-2)^2$ polynomial equations whose solutions give the parameterisation of the complex $n\times n$ Hadamard matrices. It is shown that in general the Hadamard matrices depend on a number of arbitrary phases and a lower bound for this number is given. The moduli equations define interesting geometrical objects whose study will shed light on the parameterisation of Hadamard matrices, as well as on some interesting geometrical varieties defined by them.

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