Fig. 1: Magic distillation bounds from majorization of Wigner quasi-distributions.

This plot shows distillation upper bounds for qutrits obtained from majorization on unital protocols. The constraints are plotted as a function of the depolarizing error ϵ for a noisy Strange state (Eq. 23). The bound R_∞ follows from a Lorenz curve analysis presented before Eq. 32, while the bound R₁₀ comes from single-shot entropies on the Wigner quasi-distributions, as discussed in the derivation of Eq. 52. Numerical bounds R_num are obtained by using the full set of majorization constraints. Bounds R_∞, R₁₀, R_num all provide stricter constraints than mana¹⁰¹ and max–thauma \({\theta }_{\max }\)¹¹⁶ bounds for noisy Strange states.