I was explaining to a colleague that you can't use EPR pairs to communicate information, as it violates the no-communication theorem. This lead me to thinking... If I have let's say 1,000,000 EPR pairs shared with someone far away. We agree ahead of time that if I perform a rotation $\theta$ on my qubit, then I mean to communicate the bit $0$, and when I perform the rotation $\phi$, then I mean to communicate the bit 1.
We agree that at some time in the future (assume we have synchronized clocks), that I will perform the same rotation on all 1,000,000 of my EPR pair halves. After some agreed upon time, the holder of the other 1,000,000 pair halves measures his qubits to predict which rotation I made on my qubits. Then with high probability they can guess the message I wanted to send.
I know there is something wrong in this configuration, but I can't point it down. If this would be possible, then I could communicate faster than light...
Can anyone point out the error in my reasoning?