Nonclassical state of light

A state of light is nonclassical when it is not a classical mixture of coherent states. The Glauber-Sudarshan representation states this criterion in phase space. Examples include nonvacuum number states and quadrature squeezing states. A coherent state is on the classical boundary despite its vacuum fluctuations; thermal light is a classical mixture despite its non-Poisson fluctuations. None of these nonclassicality witnesses is a necessary condition for nonclassicality.

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