I’ve been working on quantum computing and quantum communication for 15 years now and what I really want people to know is that entanglement is “beyond classical correlation.” Correlation which is not beyond classical is shaking up a shoebox with a pair of gloves in it, and having two people take the gloves far away from each other to then observe what hand they got. They then understand the hand the other has. There…
Decoherence is sort of analogous to air. It's so ubiquitous in your life that you don't really think about it, but you'd notice immediately if it was removed. Being steeped in air your whole life has twisted your physical intuitions. That's why Aristotle thought "objects come to rest" when actually objects move at constant speed unless acted upon by a force. Similarly, being steeped in decoherence has twisted your physical intuitions. Like thinking "adding more ways for something to happen must make it more likely" or "a particle's position is independent of its momentum" or "I can measure an object without affecting it". But actually different paths can interfere, and momentum is the Fourier transform of position, and measurements apply phase noise.
Decoherence is so ubiquitous that it's a huge challenge to engineer systems that suppress it. This is why quantum computers are so hard to make, and why quantum error correction has so much more overhead compared to classical error correction. Classical error correction only has to fix bit flips, and it can do so by making phase flips worse (which it does). Quantum error correction has to simultaneously fix bit flips and phase flips.
When two particles are entangled, rotating one around the X axis by an angle A and the other by an angle B and then measuring produces measurement results that agree with probability cos^2(A-B). Same as the probability of a photon with polarization angle A passing through a polarizing filter with angle B. Decohere the entanglement before the rotations, and the measurements will instead agree with probability cos^2(A)cos^2(B) + sin^2(A)sin^2(B). Note that cos^2(A-B) = cos^2(A)cos^2(B) + sin^2(A) sin^2(B) + 2 cos(A) cos(B) sin(A) sin(B), meaning decoherence is taking away the 2 cos(A) cos(B) sin(A) sin(B) interference term. That's the downgrade. That's what makes your best possible CHSH win rate drops from 85% to 75%. If entanglement allowed sending messages, the initial CHSH win rate would be 100% instead of 85%.