However a quantum machine that would be capable of post-selection is described by the more powerful class PostBQP = PP, and we know that PP includes NP, so this justifies your analogy.
I don't know much about quantum physics or quantum computing, so I may be mistaken, but it seems to me that post-selection is more of a philosophical construct than something that is physically possible, though.
I've seen post-selection demonstrated in a laboratory. It definitely isn't just a philosophical construct, except inasmuch as what it says about time making people want it to be less than real, and logic doesn't work that way.
As for whether you could make a PostBQP-capable computer, though.. I don't think so, at least in the most general case. I don't understand this nearly well enough to be sure, but from what I've heard, tricking causality like that has the problem that you're increasing the chance of your circuitry failing right along with the chance of getting the right result, and quantum computers are already hard enough.
But we do know that BQP \ P is non-empty, which is what I was trying to say. In fact, factoring large integers lies in BQP \ P, and is also the basis of some commonly used encryption algorithms.
No, we don't know that either. For all we know, we could have BQP = P: today, we don't know any algorithm in P to factor integers, but that's not a proof that it doesn't exist. If we had such a proof, as mcpherrinm points out this would directly lead to a proof that P != NP (since we DO know that factoring is in NP).
Also, I don't mean to pile on, but this wasn't what you were trying to say in the paragraph I quoted: in that paragraph, you said that we just had to pick problems outside BQP to make cryptography work despite quantum computers. I don't know if that's what you had in mind, but for such an algorithm to be tractable, it should at least be in NP (nobody with a deterministic computer wants to spend an exponential amount of time establishing an SSL connection): so the mathematical statement is whether NP \ BQP is non-empty. Did I miss something?
However a quantum machine that would be capable of post-selection is described by the more powerful class PostBQP = PP, and we know that PP includes NP, so this justifies your analogy.
I don't know much about quantum physics or quantum computing, so I may be mistaken, but it seems to me that post-selection is more of a philosophical construct than something that is physically possible, though.