As you say in your last comment, this is clearly fictional as a theorem, but the argument has been raised in less fictional works. The "theorem on uncertainty" phrase probably is intended to hint to the uncertainty principle and/or the no-cloning theorem from quantum mechanics. For instance, Scott Aaronson writes

Does quantum mechanics (specifically, say, the No-Cloning Theorem or the uncertainty principle) put interesting limits on an external agent’s ability to scan, copy, and predict human brains and other complicated biological systems, or doesn’t it?

I regard the above as an unsolved scientific question, and a big one. Many people seem to think the answer is obvious (though they disagree on what it is!), or else they reject the question as meaningless, unanswerable, or irrelevant.

Note that he is far from being the first to ask the question (e.g. Alan Turing did in 1951), although Aaronson did perhaps help sharpen it.

So with respect to brain function, this "theorem" is just a hypothesis, and it may well prove to be false. The empirical evidence on the relevance of quantum processes for understanding brain functioning is questionable at best, although you do see occasional "breakthroughs" reported in the press, e.g. on Orch OR; see the long list of comments under the abstract for the actual paper for more.

As you say in your last comment, this is clearly fictional as a theorem, but the argument has been raised in less fictional works. The "theorem on uncertainty" phrase probably is intended to hint to the uncertainty principle and/or the no-cloning theorem from quantum mechanics. For instance, Scott Aaronson writes

Does quantum mechanics (specifically, say, the No-Cloning Theorem or the uncertainty principle) put interesting limits on an external agent’s ability to scan, copy, and predict human brains and other complicated biological systems, or doesn’t it?

I regard the above as an unsolved scientific question, and a big one. Many people seem to think the answer is obvious (though they disagree on what it is!), or else they reject the question as meaningless, unanswerable, or irrelevant.

Note that he is far from being the first to ask the question (e.g. Alan Turing did in 1951), although Aaronson did perhaps help sharpen it.

So with respect to brain function, this "theorem" is just a hypothesis, and it may well prove to be false. The empirical evidence on the relevance of quantum processes for understanding brain functioning is questionable at best, although you do see occasional "breakthroughs" reported in the press, e.g. on Orch OR; see the long list of comments under the abstract for a review paper for more. On the other hand, other researches continue to pursue brains simulators like the Blue Brain Project, although it's computatinally very expensive just to simulate a part of a rat's brain.