= CHSH Tsirelson bound
{c}
{title2=$|S|\leq2\sqrt2$}
For dichotomic <observables> with $A_i^2=B_j^2=I$, let $\mathcal B=A_0\otimes(B_0+B_1)+A_1\otimes(B_0-B_1)$. Expanding gives $\mathcal B^2=4I-[A_0,A_1]\otimes[B_0,B_1]$. Each commutator has <operator norm> at most two, so $\|\mathcal B\|^2\le8$ and $|\langle\mathcal B\rangle|\le2\sqrt2$. Appropriate spin measurements of a <Bell state> attain equality. The local hidden-variable bound of the corresponding <CHSH inequality> is two.
Back to article page
