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
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
