Operator-entropy growth for the seven-state counterexample

Determine the growth of the positive-index Rényi and von Neumann operator entropies for the seven-state involutive Yang–Baxter gate without dual unitarity constructed in Section 11.

Background

The seven-state construction proves an exponential lower bound on the exact operator Schmidt rank of an evolved one-site operator. However, the proof does not control the normalized operator-Schmidt weights, so it does not determine the corresponding Rényi or von Neumann operator entropies. The paper explicitly identifies this entropy growth law as unresolved.