13 problems

Global monotonicity conjecture. The Kubo–Mori update can only increase the log-likelihood:

Let $S^{\mathrm{Keyl}}$ denote Keyl's rate function, and let admissible tomographic rate functions be rate functions arising from consistent tomography protocols. The Keyl conjectu…

Let $\rho^0$ be the unknown quantum state, let $\operatorname{rank}(\rho^0)$ denote its rank, and let $\tilde{\rho}^{dens}_{N/4}$ be the density estimator with tuning parameter…

A tomogram is a collection of marginal distributions obtained by integrating a phase-space function along trajectories of a dynamical system; here the trajectories arise from an in…

Uniform lower-bound conjecture. For any fixed rank $r$, $lambda_{min}$ is larger than a fixed constant for all states of rank $r$, regardless of the number of ions.

Reduced settings hypothesis. For Pauli measurements, the MSE of low-rank states should concentrate when only a small number of measurement settings is used.

The tomography strategy concerns estimating an unknown quantum state on $n$ copies, in dimension $d$, with target accuracy $\eps$, and has runtime currently bounded by a quantity o…

Complexity conjecture. The $b1$-permanent has the same computational complexity as the usual permanent for every $b1>0$.

Let $n$ complex unit vectors in $\mathbb{C}^m$ form an $(n,m)$-frame if they constitute a finite complex equiangular tight frame, with mutual inner products satisfying … It is know…

Let $n$ be a positive integer. A rank-1 observable is an observable of the form $zz^*$, and a collection of such observables is injective modulo phase if its quadratic measurements…

Roy–Singh's N+1 marginal theorem. The $N+1$ marginals of $W$ can be reproduced by positive phase-space densities, but no more than $N+1$ marginals can be so reproduced for arbitrar…

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…

Optimality conjecture for conditional SIC-POVMs. Conditional SIC-POVMs are optimal whenever they exist, in particular by minimizing the determinant of the average covariance matrix…