The paradox arises when this system falls into a black hole causing the information to devolve into a single state.
Or... maybe it doesn't devolve into a single state at all. We can't actually see what goes on inside of black hole... but if our assumptions about what actually happens appear to create a paradox, then maybe it's our assumptions aren't valid, rather than the original basic concept of what a black hole supposedly is. I believe that the concept that black holes are necessarily singularities may be flawed. Space is so distorted by gravity in their vicinity that straight lines which intersect their event horizon never exit it, but I do not think that means that all of a black hole's mass is necessarily at its center, or even necessarily collapsing inexorably towards its center. Its center is just its center of mass.
And yeah, I know that astrophysicists with a vastly more qualifications than I have came up with these ideas, but in the end, an argument from authority does not make one actually right.