The pool's estimated isn't drained, but its "objective entropy" is reduced; ie. the amount of state leaked to the outside goes up. Of course, practically you can't recover that information within a usable timespan, so it's academic.

Actually, now I sort of wonder what would happen if you encrypted a quantum superposition so that to determine which branch was taken would require reversing an operation using, at the lower bound, more computation than is available in the universe. Would it hold, or collapse/decohere?