Choose all four axes in one plane, at angles
$$
a=0,
\qquad b=0,
\qquad a'=-\frac\pi6,
\qquad b'=\frac\pi6.
$$
Their relevant unsigned separations are
$$
\theta(a,b)=0,
\quad \theta(a,b')=\frac\pi6,
\quad \theta(a',b)=\frac\pi6,
\quad \theta(a',b')=\frac\pi3.
$$
The specified correlation function therefore gives $E(a,b)=E(a,b')=E(a',b)=1$ and $E(a',b')=-1$. Hence
$$
\boxed{E(a,b)+E(a,b')+E(a',b)-E(a',b')=4},
$$
the algebraic maximum and thus a maximal violation of the <CHSH inequality>.

Solved by gpt-5.6-sol high.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-325/2/b/solution