[YayamiOmate]

It the paragraph setting the premise correct?

"The problem is this: The laws of quantum mechanics insist that information about the past is never lost, including the record of whatever fell into a black hole. But Hawking’s calculation contradicted this. He applied both quantum mechanics and Albert Einstein’s theory of gravity to the space around a black hole and found that quantum jitters cause the black hole to emit radiation that’s perfectly random, carrying no information. " I always thought that amount of information about current description of it must be conserved. It's differet than history of the state evolution. IMO simplest QM experiment contradicts this statement: if you pass a linearly polarized filter on a rotated filter you get a random result. You can't infer original state. It's like mas conservation in box of eggs. If you shake it, the amount of eggs is the same, it's state is different and untrackable.

So in my understanding the blackhole was a perfect scrambler. It carries the same amount of information is distribution random. Or the number of bits must stay the same but their distribution changes. That might be slightly different from amount information definition in Shannon sense.

Was my understanding wrong all along?

[jerf]

If you have a complicated qubit that collapses (by whatever mechanism) into a pure 1 or 0, you still have a qubit with a history in the world that is continuous. A complicated qubit doesn't carry any more information than the pure 1 or 0 in this particular sense.

The concern about black holes is that you toss a bunch of qubits (in the mass) in, and then there is a discontinuity; qubits with no particular relationship to anything that went in come off the surface as Hawking radiation. It isn't just that the qubits are really, really "scrambled"; thing getting too scrambled to put back into their original state in any feasible amount of work is a thing that happens all the time in the non-black-hole world anyhow. But there's still continuity, and the theoretical possibility of restoring the original state. The concern with black holes is that it isn't even theoretically possible to put together the original states. (It's going to be practically impossible either way.) There's a discontinuity in the qubits evolution, where they seem to entirely disappear from the universe at one place ("in" the black hole, for whatever exact definition of that ends up making sense; for this particular discussion, that's a complicated question!), and suddenly re-emerge with no relationship to any past state in the Hawking radiation. That discontinuity is the concern.

If I have this right.

(Stepping even further out of my comfort zone, I think part of the problem with this "discontinuity" is ultimately the same problems you learned about in calculus class with discontinuities in functions. Our understanding of QM is mostly expressed in differential equations. Those equations can't tell us about what happens if there are actually discontinuities in the world. In their own way they're as bad as the singularities that appear in relativity for black holes. It means "anything" could happen.)

[usgroup]

I'd hazard to guess that "information" implies "not uniformly random", and "uniformly random" implies "no information". That the black hole ripples random implies that the input is in part "converted" to uniformly random and thus by the implications above that information is lost.

At least that's how I'd interpret your paragraph.

[saagarjha]

> "uniformly random" implies "no information"

You can have something that when observed appears to be uniformly random but can be transformed into something that is not. Consider a Hadamard transform applied to |+>.

[jacobush]

Or decryption?

[cbzbc]

Possibly - though decryption relies on other information held elsewhere (the keys), so I imagine within physics it then turns into a hidden variable problem.

[usgroup]

I feel that the operative difference is between “being” and “seeming” uniformly random.

[misja111]

You are right, there exists no such law in quantum mechanics.

But even if it would exist, then there would still be no justification for assuming that this law should still hold in a place as extreme as a black hole. A black hole is by its very nature a place where our current laws of physics are not defined.