# Does this setup violate relativity?

Suppose Alice needs to transmit a bit of information about something which happened just before $$t = 0$$ to Bob who is light years away from Alice. Entangled pairs of qubits, $$\left|00\right> + \left|11\right>$$ (after normalising) is being created at the midpoint of Alice and Bob and shared. There exists a time $$t = -T$$ such that the half entangled pair created at $$t = -T$$ reaches Alice and Bob at $$t = 0$$. Assume that there is a setup with Bob which creates some sort of interference of the qubits he receives. Now, if the required bit to transmit is 0, Alice does nothing. However, if the required bit to transmit is 1, Alice does a measurement of the qubits (half the entangled pairs) which she receives from time $$t = 0$$. It means that if Alice gets a 0, the corresponding qubit which Bob has is 0 (similarly with 1). Now, this means that Alice has information of Bob's qubit and the interference stops at $$t = 0$$. If Bob keeps seeing interference after $$t = 0$$, it means that the bit was 0. If Bob sees that the interference stops at $$t = 0$$, the bit was 1. It looks like information got transmitted faster that the speed of light. Can someone please explain why this is wrong?

I think you need to be more specific on this point. From Bob's perspective his qubit is simply a mixed state in the computational basis $$\rho_B=\frac{1}{2}|0\rangle\langle 0|+\frac{1}{2}|1\rangle\langle1|$$ so he will not be able to perceive any interference effects.