= Coplanar qubit realization of the chained Bell inequality
{title2=$I_{N,2}=2N\sin^2(\pi/(4N))$}
On $|\Phi^+\rangle$, measure $\sigma_z\cos\theta+\sigma_x\sin\theta$, assigning <bit> $a$ to eigenvalue $(-1)^a$. Choose Alice's angles $2(i-1)\delta$ and Bob's angles $(2i-1)\delta$, with $\delta=\pi/(2N)$. The <Bell state> correlation is $\cos(\theta-\phi)$. Each adjacent disagreement term and the last agreement term therefore has <probability> $\sin^2(\pi/(4N))$. For $N\geq2$, their total violates the <chained modular Bell inequality> bound one, and it tends to zero as $N\to\infty$. At $N=1$ the value is exactly one.
// Target: probability-and-statistics.bigb
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