8 problems

Let $\rho$ be a bipartite state. The quantities $E_{\chi,2}(\rho)$ and $E_{\kappa,2}(\rho)$ are the level-two quantities in the $\chi$- and $\kappa$-hierarchies, respectively, and…

Let $\rho=\rho_{AB}$ be a state. The quantities $E_{\chi,p}(\rho)$ are the $\chi$-quantities defined by the hierarchy at level $p$, and $E_{\kappa,p}(\rho)$ are the corresponding…

For each integer $n\ge 3$, let $(\alpha_1,\ldots,\alpha_n,\beta_1,\ldots,\beta_n)$ be the parameters used in the paper's construction of PPT states in $M_n\otimes M_n$, and let the…

Let $n\ge 3$. Consider the PPT states constructed in the paper, with parameters chosen suitably, having bi-rank $(n^2-1,n^2-2n+3)$ in the $n\otimes n$ system. Conjecture. With a su…

Let $\rho_{AB}$ be a quantum state on $\mathds{C}^{d_A}\otimes\mathds{C}^{d_B}$, and suppose that it has positive partial transpose, meaning…

Let $d$ be a positive integer, and let an extremal PPT-BE state be an extremal positive-partial-transpose bound-entangled state in $\mathbb{C}^d\otimes\mathbb{C}^d$ with full local…

Let $\rho$ be a $3\times3$ edge state, meaning a positive-partial-transpose entangled state whose range contains no product vector, and let its birank be $(5,5)$, namely…

Leinaas–Myrheim–Sollid conjecture. For all $M,N>2$,