No, you can't learn anything from observing the other half of an entangled particle pair anyway.
That's the "No-communication theorem". However you analyse it, and whatever sequence of observations you or your partner with the other particle do, what you observe is in all ways indistinguishable to you from random noise, until you get to compare with what the other person observed for their observations of the companion entangled particle, and then you see correlations.
Entanglement is very fragile anyway and easily broken. Shouldn't think you could preserve it while falling into say, a stellar sized black hole, very hard anyway.
But it might be possible to maintain it with one particle going into a very large black hole where crossing the event horizon is something you wouldn't even notice as the person or particle falling in. So the idea seems sound to that extent, except for that matter that you can't communicate anything and the correlation is useless for deducing anything about what happened inside the black hole, you only see it if somehow you can recover it.
If somehow you could recover the particle from the black hole, FTL communication or travel or some such, you could do the experiment and cross correlate the observations as a way to test to see if you did indeed manage to maintain entanglement.
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Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
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