A question on calculating entangled spin probability

[rede96]

I was trying to understand the QM tests done to show the violation of Bell’s inequality. In the example given this was done by testing the polarization of entangled photons which were positively correlated.

So in the example Alice and Bob are detecting the polarisation for the two entangled photons, using 3 detectors chosen at random, which are at angles of 0 degrees, 120 degrees and 240 degrees.

I was told that the quantum rule to predict the number of matches (e.g. both detected the same spin or both do not detect same spin) was cos^2(Alice's Angle - Bob's Angle)

As these angles are all equidistant then it is easy to see that the overall result will be 0.25 without doing all the individual test, as each individual test’s probability is 0.25

But let’s say the three detectors being used were at angles 10, 60 and 200?

Doing it long hand, i.e. calculating each individual test and adding up all the matches I get appx 0.66

But how would I calculate the expected result without doing all the individual tests? (so I can check I am doing it right!)

Thanks.

 

[rede96]

I've got the answer now thanks.