9 problems

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…

Analytic-properties conjecture. The function $D_{1,\dots,m}$ is meromorphic in $\lambda_1,\dots,\lambda_m$, with at most simple poles when

Let $\mathcal{H}_a$ be a Hilbert space of dimension $d_a$, let $\mathcal{H}_b$ be a finite-dimensional Hilbert space of dimension $d_b$, and let $\rho$ be a density matrix on…

Maximal-QMI upper-bound conjecture. The red points representing $\textrm{Max}[QMI]$ should lie on the upper bound black curve, and any deviation should arise solely from finite sam…

Consider reduced density operators $D_N$ of RSOS models in topological sectors with quantum dimension $d_q=1$, where the nearest-neighbour two-site correlations in a given transfer…

Optimal-order conjecture. Both the stability estimates and the convergence rates obtained for reconstructing the density matrix from the data are of optimal order under the given a…

Let $\rho$ be a density matrix of a one-qudit system of dimension $d$, with diagonal populations $\rho_{m,m}=\langle\beta_m|\rho|\beta_m\rangle$ for $m=1,\ldots,d$. Let…

Entropy comparison conjecture. The entropy of the quantum-addition mixture is at most the entropy of the ordinary weighted mixture:

Let the density matrix be the reduced density matrix of a contiguous block of bulk spins in an AKLT model. The model may be an inhomogeneous chain, a system on a higher-dimensional…