Fig. 3: A “heretical” family of Lorenz curves.
From: Constraints on magic state protocols from the statistical mechanics of Wigner negativity
Traditionally, Lorenz curves for distributions are monotone increasing cumulative functions that reach a maximum value of 1. In contrast, Lorenz curves for magic states break through the value of L(x) = 1 due to the presence of negativity in the associated quasi-distributions. The above family of curves correspond to multiple copies of noisy Strange states ρ := ρS(ϵ)⊗n (Eq. 23) for n = 2, 4, 6 within \({{{{\mathcal{R}}}}}_{\sigma }\), where \(\sigma \,=\,{\mathbb{1}}/3\). Solid lines represent pure Strange states, while dashed lines represent ϵ-noisy Strange states with depolarizing error ϵ = 0.1.
