6 problems

Let $\mathcal{C}_d$ denote the set of circulant matrices, $\mathcal{U}_d$ the set of unistochastic matrices, and $\mathcal{C}_d^2$ the set of doubly circulant unistochastic matrice…

Let $\mathcal{L}_d$ be the set of bracelet matrices of dimension $d$. A monoid is a set closed under matrix multiplication and containing an identity element $\mathbb{I}_d$. Monoid…

Consider the face of the simplex of Weyl channels determined by $(\Phi_{\mathbb I},\Phi_X,\Phi_{X^2})$, and let the star of David be the inscribed region described in the paper. St…

Let ${\cal W}_3$ be the simplex of Weyl channels, and let … be the face spanned by the channels $\Phi_{\mathbb I}$, $\Phi_X$, and $\Phi_{X^2}$. Let $\mathbb{H}_3$ be the hypocycloi…

Let $\mathcal{B}_N$ be the Birkhoff polytope of $N\times N$ bistochastic matrices, let $\mathcal{U}_N\subset\mathcal{B}_N$ be the set of unistochastic matrices, and let…

Let ${\mathcal U}_4$ be the set of unistochastic matrices of order $4$, and let ${\mathcal B}_4$ be the Birkhoff polytope of doubly stochastic matrices of order $4$. Star-shapednes…