This question is motivated by the issue of information retrieval from black hole

Question

This question is motivated by the issue of information retrieval from black holes, but it is essentially a question about quantum information.

It is widely believed (in certain circles) that the information about the history of black hole formation is continuously leaked out as the black hole is evaporated, and is encoded by the Hawking radiation quanta. This way one does not lose information when the black hole is completely evaporated, and furthermore one does not need to postulate some implausible ways in which macroscopic amount of information is stored in an increasingly microscopic object, only to be somehow released at the very last stage of the evaporation process.

To make this more quantitative, I am wondering if similar questions were asked in the quantum information community. Suppose you have an encrypted message of a certain length which is revealed to you over time, and you are trying to decode it. Obviously the more time passes the more information you can have about the message, and when you reach a time which scale with the size of the message you are expected to gain access to the full information. I'm looking for some more quatitative knowledge about this question. For example:

For a generic decoding, is it known how much time you need in order to gain access to a finite fraction of the information? Are there some universal results about the asymptotics of such process (in the spirit of "critical exponents")?

Are there bounds on optimal encoding, whose purpose would be to delay a release of a finite fraction of the information to later and later times? In particular, can there be encoding which releases a finite fraction of the information only at the very last stages of the decoding?

I realize this is probably an hopelessly pedestrian question, pointing me towards some review literature might be the way to go in such case.

Edit: Thanks everyone for your answers, they all were useful in different ways. The question was vague enough for it not to have a single correct answer, but I'll choose Peter's because he somehow managed to read my mind (though there was no way to tell from the way the question was phrased). Hope to ask more precise questions on related topics in the future.

Explanation / Answer

You've clearly read the paper of Hayden and Preskill: Black holes as mirrors: quantum information in random subsystems, since you mention it in the comments. Another quantum information phenomenon related to your question is "information locking" (see this and other papers), where you can arrange things so that all the information in a quantum system of n bits is essentially inaccessible until you get the last logn bits. There are several papers about papers about "locking" information or entanglement, and I suspect some of your questions may be answered in one of these.

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