Based on my knowledge of quantum entanglement, I can set up a scenario which leads to a contradiction with the No-communication theorem. Please help me find the flaw.
Suppose Alice wants to communicate a message to Bob (1 or 0). Alice has 100 electrons (which we will call a_1, a_2, ..., a_100) and Bob also has 100 electrons (which we will call b_1, b_2, ..., b_100). Each one of Alice's electrons is entangled to exactly one of Bob's electrons such that a_n and b_n have opposite spin. First, Alice measures the spin of each of her electrons along the z axis and records each result. Then, if Bob wants to communicate a zero, he does not measure the spin of his electron, so that when Alice measures her's a second time about the z axis, she gets the same results as in her first measurement. If Bob wants to communicate a 1, he measures the spin of each one of his electrons about the x axis so that when Alice makes a second measurement of each of her electrons about the z axis, her results should not be correlated to the first measurement she took. If everything I said were true, this would provide a very high probability for Bob to correctly transfer a bit of information to Alice, potentially at faster than light speeds which violates the No-communication theorem.
