7 problems

Irrational-angle counterexample conjecture. It is impossible to find a counterexample satisfying $\varphi_0\notin 2\pi\mathbb{Q}$.

Let $\Delta^3$ denote the probability simplex, let $\mathsf{derv}(\lambda)$ be the set of achievable derivatives at $\lambda$, let $S_4$ be the permutation group on four elements,…

Exponential stabilization conjecture. The first controller almost surely exponentially stabilizes $(\rho_t,\hat{\rho}_t)$ to $(\boldsymbol\rho_{\bar n},\boldsymbol\rho_{\bar n})$ w…

Controllability-diameter conjecture. For every such Hamiltonian, the implication

Let $\Sigma$ be a finite-dimensional quantum control system on $\mathbb{C}^n$ of the form … where $A$ and the $B_i$ are skew-adjoint matrices, and normalize the drift by…

Optimal-angle no-improvement conjecture. At the optimal homodyne angle,

No-improvement conjecture. The coherent-classical estimation cost satisfies