HW 10: Exercise 1

HW 10: Exercise 1

by Ali Essonni -
Number of replies: 1

Hello,

I am really stuck on the question a of exercise 1.

I don't really know what the probability that we have to compute represents, nor the choice of alpha and beta that are given, and the relation that all this has with Psi.

I've tried to watch the videos to see if there is something I'm missing, but it turns out I don't understand the whole part about CSHS inequality. When computing the correlation coefficient, where do the probabilities go?

If someone could explain this part, would be very much appreciated.

Thanks

In reply to Ali Essonni

Re: HW 10: Exercise 1

by Nicolas Macris -
Hi
this probability p(a,b | alpha, beta) is the probability that Alice records a = +1 or -1 and Bob records b= +1 or -1 when they do a measurement in their basis corresponding to the angles alpha and beta.

Apply the measurement postulate (Born rule).

For example p(+1, -1 | alpha, beta) = | < alpha | \phi_A > |^2 |< beta_\perp | \phi_B > |^2

Similarly p_A(+1 | alpha) = | < alpha | \phi_A > |^2 and p_B(-1 | beta) = |< beta_\perp | \phi_B > |^2

Thus you see that p(+1, -1 | alpha, beta) = p_A(+1 | alpha) p_B(-1 | beta)

Similarly for all other cases (there are four cases).

Thus we have the same same "locality property" as in LHV theories (except that here there is no hidden variable so there is no lambda and no integral over lambda so its simpler) and you can follow excatly the same derivation than in class to conclude that
| X | < 2.

Hope this helps. Otherwise we are available during exercise session.

best
N.M