[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.