Classification of further comparison sets

Identify and classify further comparison sets satisfying the tensor-product and positive-polar tensor conditions of the paper’s strong-superadditivity criterion, in order to construct additional correlated-catalytic monotones for quantum resource theories.

Background

The paper proves a general criterion showing that regularized relative-entropy measures are strongly superadditive when their underlying comparison sets satisfy specified structural properties, including tensor closure and positive-polar tensor closure.

Beyond the PPT hierarchy, the authors explicitly leave unresolved the task of finding and classifying additional comparison sets with these properties. Such sets could generate new additive and strongly superadditive monotones applicable to correlated catalysis in other resource theories.