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    $\begingroup$An excellent question but I doubt the answer will be very intuitive. You might want to read the book "The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics" by Leonard Susskind. My understanding is that the information is encoded in the outgoing Hawking radiation but that no one knows how it is encoded. Similarly when you burn a book, the information is still encoded in the smoke, ashes and gasses that are emitted, but no one knows how exactly.$\endgroup$
    – FrankH
    CommentedNov 22, 2011 at 19:48

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