As the sibling hinted at, Gisin's statement is quite sloppy and – at the very least – confuses "definite" "information"¹ (a given real number) with "uncertain" "information" (entropy), at least if you follow the definition of entropy by the book: The probability distribution for an observable that takes on (exactly) the value of a given real number with probability 1 has entropy 0.
That being said, Gisin's approach is still interesting and his results can still be valid. But he starts with the assumption that real (irrational) numbers are unphysical, i.e. that – in a sense – our observable from above can actually only take on certain (rational) values, and then he derives certain predictions from that.
¹) Putting "information" in quotation marks here because no one really knows what it is.
That being said, Gisin's approach is still interesting and his results can still be valid. But he starts with the assumption that real (irrational) numbers are unphysical, i.e. that – in a sense – our observable from above can actually only take on certain (rational) values, and then he derives certain predictions from that.
¹) Putting "information" in quotation marks here because no one really knows what it is.