- Edited
why assume it is due to a feature of the particles themselves.
There is no assumption! That is the entire point, that you consistently fail to understand; In the purely classical experiment, the coins were constructed to have exactly that property - because that is what a bit of information is - a packet of noise, riding upon a carrier.
Just think of what determines the value of any actual coin - it is not the physical "stuff", the metal substance; the metal is just the carrier of the "information" being used to determine the coin's value - but the actual information itself, is encoded, entirely within the markings on the surface - the "noise."
Shannon's greatest discovery, was the realization, that in order to be reliably detected - for any completely deterministic behavior to ever emerge, in a noisy environment - the "information" must be encoded to have, the statistical properties of white noise! In other words, instead of a picture of an actual "Head" and "Tail", you must use two different patterns of white noise, to represent/encode the "Head" and Tail" - because the noise-like encodings can be much more reliably detected, than any actual picture!
Hence, your "extra correlation" arises entirely from the fact that the auto-correlation of noise-like sequences, generate more reliably detectable, large peaks, than any other known type of encoding. Which is why "Mother Nature" appears to use them, to generate deterministic behaviors; and She generates them, out of the very Chaos itself - the noise!
And it can be amazingly easy for deterministic behaviors to emerge from the Chaos; rather than wasting time searching for it; just create it yourself! (“You” being Mother Nature), out of pure noise!