The quantum mechanical weak value $A_w=\langle \varphi \left|A\right|\psi \rangle /\langle \varphi |\psi \rangle$ of an observable $A$ is a measurable quantity associated with an observable $A$ and pre- and postselected states $|\psi \rangle ,|\varphi \rangle$. Much has been discussed about the meaning and metrological uses of anomalous weak values, lying outside of the range of eigenvalues of $A$. We present a simple proof that anomalous weak values require that the (possibly mixed) pre- and postselection states have coherence in the eigenbasis of $A$. We also present conditions under which anomalous $A_w$ are witnesses of generalized contextuality, dispensing with the operational weak measurement setup.

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• Quantum correlations in quantum information
• Quantum foundations
• Quantum information theory
• Quantum superposition
• Weak values & weak measurements