HW4 - Problem 1

Problem 1: Proving Shion’s Code is Bugged

The following strategy (slightly modified for easier math) for the CHSH game was discovered by one of your classmates in this class, yielding a 100% winrate which should not be possible. We won’t prove the optimal winrate, but we can show that this value is incorrect by computing the probabilities of success for each of the strategies and outcomes. You can assume that the angle 1.499 is rounded to 1.5, and 1.999 is rounded to 2.

  1. Consider the case where \(x=0\) and \(y=0\). Make sure to note that we are starting in the state \(\left|\Psi-\right>\) Let’s suppose Alice measures first for our analysis. What are the possible states after her measurement? There are two cases so make sure to state each one.
  2. For each of these cases, what are the measurement outcomes and probabilities for Bob?
  3. What should the probability that Alice and Bob win using this strategy be if \(x=0\) and \(y=0\)?
  4. Now let’s consider the case where \(x=0\) and \(y=1\). What are the possible states after Alice’s measurement in this case?
  5. In each of the cases, what are the possible measurement outcomes for Bob?
  6. What should the probability that Alice and Bob win using this strategy be if \(x=0\) and \(y=1\)?
  7. (Take a guess) What do you think is causing this error? If you were debugging this code where would you try to start?