I think you are folding two things together that are related but not the same. Hidden variables are about the state of an entangled system. The uncertainty prin

I think you are folding two things together that are related but not the same. Hidden variables are about the state of an entangled system. The uncertainty principle can be applied to measurements taken of an entangled system but can also just refer to two quantities of a single particle such as it's position and momentum.