Tang's ℓ2-Norm Sample-and-Query Model as the Unique Classical Implementation of the Born Rule from Five Operational Axioms

Tang’s dequantisation programme established that several quantum machine learning algorithms admit efficient classical simulation when given ℓ2-norm sample-and-query (SQ) access to their input data. The specific choice of ℓ2-norm sampling—rather than uniform, ℓ1, or any other sampling rule—has hitherto been justified operationally by its polynomial-time implementability, but not axiomatically. We show that ℓ2-norm SQ sampling is the unique sampling functional satisfying five natural operational