HW4 - Problem 1

Problem 1: Hacking the CHSH Game

Consider the following strategy for the CHSH game, as opposed to the one discussed in class.

That is, both Alice and Bob will use the same strategy.

  1. Try using this strategy to play the game a couple times using the CHSH game simulator. What is your guess on the winning probability for this strategy?
  2. Consider the case where \(x=0\) and \(y=0\) as we did in class. Let’s suppose that Bob measures first for our analysis. What are the possible states after Bob’s measurement? There are two cases so make sure to state each one.
  3. In each of the cases, what are the possible measurement outcomes for Alice?
  4. What is the probability that Alice and Bob win using this strategy if \(x=0\) and \(y=0\)?
  5. Now let’s consider the case where \(x=0\) and \(y=1\). What are the possible states after Bob’s measurement in this case?
  6. In each of the cases, what are the possible measurement outcomes for Alice?
  7. What is the probability that Alice and Bob win using this strategy if \(x=0\) and \(y=1\)?
  8. Assuming that all four input pairs for \(x\) and \(y\) are equally likely, what is the probability the Alice and Bob win the game?