# PromiseBQP and expectation values of operators

This question is regarding The Equivalence of Searching and Sampling by Aaronson. In page 4 he makes the following statement,

... a difficult and unsolved meta-question is whether PromiseBPP = PromiseBQP implies SampP = SampBQP. Translated into “physics language,” the question is this: suppose we had an efficient classical algorithm to estimate the expectation value of any observable in quantum mechanics. Would that imply an efficient classical algorithm to simulate any quantum experiment, in the sense of sampling from a probability distribution close to the one quantum mechanics predicts?

I have trouble understanding this statement. From the definition of PromiseBQP I don't see how PromiseBPP = PromiseBQP means an efficient classical algorithm to estimate the expectation value of any observable in quantum mechanics. Any ideas how this connection can be made?