Ultraweak superposition in nonclassical simplicial theories

Construct an explicit non-classical simplicial theory that satisfies ultraweak superposition as defined by D’Ariano et al., thereby resolving whether such an example exists.

Background

The paper reviews a hierarchy of superposition principles introduced in earlier work, including ultraweak superposition. It states that non-classical simplicial theories fail to satisfy the stronger weak and strong forms, but that the existence of a non-classical simplicial theory satisfying ultraweak superposition remains unresolved. This is presented as an explicit missing example in the prior framework.

References

However, an explicit example of a non-classical simplicial theory satisfying ultraweak superposition remains unknown.

— No extension of the Quantum Tensor Product admits a Superposition principle  (2608.17572 - Fiorentino et al., 18 Aug 2026) in Appendix, Section “Superposition in D'Ariano et al., 2020”