PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Quantum states, measurement and entanglement · Quantum states, measurement and entanglement
Quantum Information and Technology, Ch Nonlocality: EPR, Bell inequalities and the CHSH game
Problem
Alice and Bob share many copies of ∣Φ+⟩=(∣00⟩+∣11⟩)/2, one qubit of each pair held at each of two distant stations. Someone argues: "Alice measures her qubit in the Z basis on every run. She then discards, without telling Bob, every run in which her outcome was 1, keeping only the runs where she got 0. In the kept runs Bob's qubit is ∣0⟩ with certainty, so if Bob looks only at those same runs he will see his Z-outcome equal to 0 every time, a striking change from the 50/50 result he gets when Alice does not do this. By choosing whether or not to apply this discarding rule, Alice can therefore send Bob one bit of information instantaneously, since Bob's statistics change according to her choice."
((a)) Find the error in this argument.
((b)) State, using the partial trace, what is actually true of Bob's statistics whatever Alice does to her own qubits.
((c)) Say what would have to happen for Bob to be able to make use of the correlation the argument is relying on.