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Manfred comments on Could/would an FAI recreate people who are information-theoretically dead by modern standards? - Less Wrong Discussion
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From the perspective of someone looking back at the past, measurement erases information. So when the dirt measures your brain, some of the information about what those atoms were doing before - position, momentum, spin, etc. is erased.
Example: If you take a bunch of spin-up atoms and measure them along the left-right axis, they will no longer be spin-up. Measurement erased the information that was there before. Similar principles are what make quantum cryptography work - if I sent you a spin-up atom and then a spin-right atom as the key, the attacker doesn't know which axis to measure for which atom, so they end up erasing part of the information when they measure the key.
In the quantum cryptography case, the attacker can be said to have "lost information" in the measuring because the sender still has that information (and the receiver has half of it, if I remember correctly). So it's still relevant. But for a datum about the brain to be lost irrecoverably, it has to have never affected anything, including macroscopic facts about my brain, and it cannot have been determined by any macroscopic facts about my brain. Which means the datum never actually existed.
It exists only statistically - information seems to be more like entropy than like energy. That's quantum mechanics. If you measure an atom to have spin up, it COULD be because it was alway spin up, or it could be that it was spin anything-but-down and you just got lucky. You might say "but since the fact that it was spin-x didn't affect the result, how do we know it existed at all?" Well, that's what bell's inequality is for, basically. The data in your brain isn't a hidden variable, it's part of the quantum state, and so is subject to being messed with when measured.
This looks like a fascinating concept that I'll have to read up on.