3 problems

Majorization conjecture along the family $\widetilde{W}_u$. There is a Wigner majorization order along the family $\widetilde{W}_u$ only when $u>1/2$.

Majorization conjecture for $\hat{\rho}_0$. Any mixed state with a positive Wigner function is majorized by $\hat{\rho}_0$ under the Wigner majorization ordering.

Power-universality support conjecture. Under these support conditions, $(\rho,\sigma)$ is power universal in the semiring. The claim is part of a sufficient, though not expected to…