8 problems

Let $S=\{A_1,\ldots,A_g\}\subseteq M_n(\mathbb{C})$ satisfy condition $C1$, meaning that words of some common length span $M_n(\mathbb{C})$, and let $\Gamma_L$ be the associated ma…

Positivity and definiteness conjecture. The dominant eigenvalue $\eta$ is real and positive, and

Generic MPDO conjecture. For a generic' MPDO, there exists a constant $c>0$ such that for any tripartition $ABC$ in which $B$ separates $A$ from $C$ by distance $\ell$,

Closedness conjecture. Except for the trivial cases in Proposition, $\operatorname{uMPS}(D,d,N)$ is only closed if it fills the ambient space $\operatorname{Cyc}^N(\mathbb{C}^d)$.

Let $L$ be a linear space of $D\times D$ matrices, and let $L^k$ denote the linear space spanned by all products of $k$ matrices in $L$. If … for some $k$, then … for all…

Let $\Psi$ be a translation-invariant $N$-qubit matrix product state with open boundary conditions and bond and physical dimensions $D=d=2$. A reduced density operator on a chain o…

Let $N\geq 4$. An improper marginalization maps a translation-invariant $N$-qubit matrix product state variety $\overline{\operatorname{OB}}(2,2,N)$ to…

Forward-backward correlation conjecture. There exists a function $f(D_{eff})$ such that