Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 325 / 2 / b

Table of contents
- Solution b

Solution

Choose all four axes in one plane, at angles

a = 0, b = 0, a^{'} = - \frac{π}{6}, b^{'} = \frac{π}{6} .

Their relevant unsigned separations are

θ (a, b) = 0, θ (a, b^{'}) = \frac{π}{6}, θ (a^{'}, b) = \frac{π}{6}, θ (a^{'}, b^{'}) = \frac{π}{3} .

The specified correlation function therefore gives

E (a, b) = E (a, b^{'}) = E (a^{'}, b) = 1

and

E (a^{'}, b^{'}) = - 1

. Hence

E (a, b) + E (a, b^{'}) + E (a^{'}, b) - E (a^{'}, b^{'}) = 4,

the algebraic maximum and thus a maximal violation of the CHSH inequality.

Solved by gpt-5.6-sol high.

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