17 problems

Let $V_1,V_2,V_3$ be the local qudit vector spaces with dimensions $d_1,d_2,d_3$, and let $n_a$ be the corresponding one-party nullities. For a tripartite state…

Let $V_1,V_2,V_3$ be the local qudit vector spaces with dimensions $d_1,d_2,d_3$, and let $n_a$ be the corresponding one-party nullities. For a tripartite state…

Let $V_1,V_2,V_3$ be the local qudit vector spaces with dimensions $d_1,d_2,d_3$, and let $n_a$ be the corresponding one-party nullities. For a tripartite state…

Let $\mathcal{G}_{n}^{c}$ be the set of all connected graphs on $n$ vertices, and let $G\in\mathcal{G}_{n}^{c}$ with $|V|=pq$. Star graph maximizer conjecture. … This asserts that…

Let $G$ be a graph with $|V|=pq$ and $m$ edges. For each edge, let $\sigma(k)$ denote the pure density matrix associated with the $k$-th edge. If $\sigma(G)$ is entangled in…

Let $G$ be a graph with $|V|=pq$, and let $entangled edges$ mean edges whose associated pure states are entangled. One-entangled-edge and common-vertex conjecture. If $G$ has only…

Let $n\geq 3$ and let $\vec{d}$ be a dimension vector. Write $P^{\mathrm{W}}_n(y)=P\left(\lvert\mathrm{W}_{n,\vec{d}}\rangle;y\right)$. Mainiero's generalized W Poincaré polynomial…

Let $n\geq 3$ and let $\vec{d}$ be a dimension vector. Write $P^{\mathrm{GHZ}}_n(y)=P\left(\lvert\mathrm{GHZ}_{n,\vec{d}}\rangle;y\right)$. Mainiero's generalized GHZ Poincaré poly…

Let $M_3\otimes M_n$ be equipped with the Hilbert-Schmidt norm, and let $I/(3n)$ denote the maximally mixed state. Consider the smallest Euclidean ball centered at $I/(3n)$ that co…

Let $\rho\in M_3\otimes M_n$ be an absolutely PPT state with $n\geq 2$, and let $\lambda_1,\ldots,\lambda_{3n}$ be its eigenvalues. Maximum-purity conjecture. The maximum purity of…

Let $\mathcal H=\ell^2(\mathbb Z^2)$ and let $P$ be the Fermi projection of a gapped Hamiltonian $H$ satisfying exponential locality. Let $\omega_P$ be the associated quasi-free st…

Let $G$ be sampled uniformly from graph states, and let $d4af$ be the set of eigenstates of the operators $X+Y$ and $X-Y$. For an $n$-qubit product state, write…

Let $\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}$, and let $\Phi:M_n(\mathbb{K})\rightarrow M_n(\mathbb{K})$ be an IPT map, meaning that its Choi matrix is invariant under partial trans…

Let $A_k$ denote the $k$-sector length of an $n$-qubit quantum state. Asymptotic sector-length conjecture. For all $k$ there exists an $n_0$ such that, for all $n\geq n_0$, every…

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 $\lvert\psi\rangle$ be a normalised complex vector in the tensor product Hilbert space … For a subsystem, $\operatorname{Tr}_B$ and $\operatorname{Tr}_C$ denote the correspondi…

Let a permutation-invariant multipartite state be given, and consider its maximal overlap with product states. The question concerns whether the product state attaining this maxima…