Non-plussed distinctness of the constructed ensembles

Determine whether the distinct ensembles constructed in the paper are also non-plussed distinct, including whether the depth-one ensemble of independent single-qubit Clifford gates is non-plussed distinct.

Background

Non-plussed distinctness strengthens ordinary distinctness by additionally requiring no support on the all-plus state. The paper notes that this strengthened property enables the removal of the binary phase layer from certain pseudorandom-unitary constructions.

The authors establish ordinary distinctness for several ensembles, including a depth-one product of independent single-qubit Clifford gates, but do not determine whether these ensembles satisfy the stronger non-plussed condition.

References

In the light of this, it would be valuable to determine whether the distinct ensembles constructed here are also non-plussed distinct, and whether the corresponding PRU constructions remain secure after removing the binary phase operator $F$.

— Distinctness threshold for pseudorandom unitaries  (2609.03065 - Raza et al., 2 Sep 2026) in Discussion and open questions, paragraph “Distinctness in stronger query models and beyond”