But doesn't this then violate "no information faster than speed of light"? I.e. You measure A at angle a, I measure B (entangled with A) at angle b, and the res

But doesn't this then violate "no information faster than speed of light"? I.e. You measure A at angle a, I measure B (entangled with A) at angle b, and the resulting distribution gives me some information about your angle a. If I repeat this with enough particles, I can be reasonably certain about what a is.