# Postselection and hardness of estimating amplitudes

Let $$A$$ be a class of quantum circuits such that

$$$$\text{Post}A = \text{Post}BQP,$$$$ where $$\text{Post}$$ indicates post-selection. Is only this amount of information sufficient to conclude that it is $$\# P$$ hard to estimate each output amplitude of a circuit in the class $$A$$, in the worst case, upto an inverse polynomial multiplicative error?

Note that it should be $$\# P$$ hard to compute each output amplitude of a circuit in $$\text{Post}BQP$$ upto inverse polynomial multiplicative error (as it is $$\# P$$ hard to compute each output amplitude of a circuit in $$BQP$$ upto the same error).