The result of the HHL-algorithm is the (amplitude-encoded) solution vector $|x\rangle$.
I was wondering, which useful information could be extracted from this solution without loosing the algorithms speedup by sampling it $O(N)$ times.
What I found is:
However, if I understand the answer to this question correctly, it should also not be possible to find the largest values efficiently.
Can you give more examples ? (Specifically I am interested in a method to efficiently determine if there are components $x_i$ of $x$ that exceed a certain limit)
