= Nonclassicality witnesses
Sufficient single-mode witnesses include a <Fano factor> $\operatorname{Var}n/\langle n\rangle<1$, an <optical quadrature> variance below $1/4$ for $[X,P]=i/2$, or <photon antibunching> with $g^{(2)}(0)<1$. Classical mixtures obey $\operatorname{Var}n\ge\langle n\rangle$, and $g^{(2)}(0)=\mathbb E(|\alpha|^4)/\mathbb E(|\alpha|^2)^2\ge1$ by nonnegative variance. The tests are sufficient rather than necessary and exclude the vacuum case when dividing by zero mean occupation.
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