= Pauli-string commutation parity
{c}
{title2=$PQ=(-1)^kQP$}
For <tensor products> of Pauli factors from $\{I,X,Y,Z\}$, let $k$ count the sites where both factors are nonidentity and different. Distinct nonidentity <Pauli matrices> anticommute, and equal or identity factors commute. Reversing the product site by site therefore gives $PQ=(-1)^kQP$. Thus two Pauli strings commute exactly when $k$ is even. The criterion applies to the perfect-correlation observables in the <GHZ theorem>.
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