Robust Hadamard Matrices, Unistochastic Rays in Birkhoff Polytope and Equi-Entangled Bases in Composite Spaces

@article{Rajchel2018RobustHM,
  title={Robust Hadamard Matrices, Unistochastic Rays in Birkhoff Polytope and Equi-Entangled Bases in Composite Spaces},
  author={Grzegorz Rajchel and Adam Gasiorowski and Karol Życzkowski},
  journal={Mathematics in Computer Science},
  year={2018},
  volume={12},
  pages={473-490}
}
We study a special class of (real or complex) robust Hadamard matrices, distinguished by the property that their projection onto a 2-dimensional subspace forms a Hadamard matrix. It is shown that such a matrix of order n exists, if there exists a skew Hadamard matrix or a symmetric conference matrix of this size. This is the case for any even $$n\le 20$$n≤20, and for these dimensions we demonstrate that a bistochastic matrix B located at any ray of the Birkhoff polytope, (which joins the center… 
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