10 problems

Universal NHCRB bound conjecture. For every such model,

Maximally mixed-state tomography conjecture. The maximum enhancement $\mathcal{R}^{\mathrm{NH}}$ is attained by orthonormal tomography of the maximally mixed state.

NHCRB dimension-bound conjecture. Based on analytical and numerical results,

Linear-GMM maximization conjecture. The linear GMM model at $\theta=0$ maximizes the ratio defining $\mathcal{R}^{\mathrm{NH}}$, and therefore attains $\mathcal{R}^{\mathrm{NH}}$.

Maximum-enhancement conjecture. The maximum collective quantum enhancement in any local estimation scenario is linear in the probe dimension $d$.

Feedback coherent-classical improvement conjecture. If there exists a homodyne angle $\theta_i$ such that

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

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

Let the channel directions be the three principal directions associated with the Pauli channel, and let a measurement and input strategy be described by bases relative to those dir…

Let $\underline{\lambda}$ denote the channel contraction parameters and let $N$ be the number of channel uses. Let…