Sublinear von Neumann operator entanglement from the braid relation

Determine whether the braid relation alone guarantees sublinear growth of the von Neumann operator entanglement for local observables in Yang–Baxter brickwork circuits, or construct a Yang–Baxter counterexample with non-sublinear growth.

Background

The paper establishes that operator Schmidt rank can grow exponentially for a seven-state involutive Yang–Baxter gate without dual unitarity, but operator Schmidt rank alone does not determine the positive-index Rényi or von Neumann entropies. The authors therefore leave unresolved whether the braid relation imposes sublinear von Neumann operator-entanglement growth.

References

At the level of operator entanglement, the most important open question is whether the braid relation alone is enough to guarantee sublinear growth of the von Neumann operator entanglement.

— On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates  (2609.05121 - Pozsgay, 4 Sep 2026) in Section 12, Conclusions

More generally, it is not known whether sublinear von Neumann operator entanglement follows from the braid relation or whether a Yang--Baxter counterexample exists.

— On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates  (2609.05121 - Pozsgay, 4 Sep 2026) in Section 12, Conclusions