= Quantum covariance
{title2=$C_{AB}=\tfrac12\langle A'B'+B'A'\rangle$}
For <self-adjoint operators> and an admissible <pure state>, the <quantum covariance> is the real, symmetrized second moment of two centered <observables>. The displayed expression uses their <anticommutator>; equivalently $C_{AB}=\operatorname{Re}\langle A'\psi|B'\psi\rangle$, which requires only the individual finite second moments. It reduces to ordinary <covariance> for commuting <observables>. For noncommuting <observables>, its definition does not assert that both have simultaneous sharp values drawn from a joint classical <probability distribution>.
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