Dequantization is relative to the input access and output task

Under the nonzero-row promise and countable-product sampling model stated in the theorem, Tang's real-matrix result matches a particular input structure: entry queries together with efficient row/column ℓ2-norm sampling, including the preprocessing and storage that provide those samplers. Its task is to sample from a specified recommendation row derived from a thresholded low-rank approximation, and its output is a sample rather than a full matrix or a classical list of amplitudes. It therefore establishes a classical counterpart for that access/task/output contract. It does not assert efficient classical simulation of arbitrary quantum circuits, arbitrary quantum-state output, or algorithms whose input model lacks the required ℓ2 samplers. Compare algorithms only after matching input access, output type, approximation metric, and charged preprocessing.