A simple proof that anomalous weak values require coherence

• URL: http://arxiv.org/abs/2303.08700v2
• Date: Thu, 26 Oct 2023 08:32:34 GMT
• Title: A simple proof that anomalous weak values require coherence
• Authors: Rafael Wagner and Ernesto F. Galv\~ao
• Abstract summary: We present a proof that anomalous weak values require that the pre- and post- selection states have coherence in the eigenbasis of $A$. We also present conditions under which anomalous $A_w$ are witnesses of generalized contextuality.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum mechanical weak value $A_w=\left\langle \phi|A|\psi \right \rangle / \left\langle \phi | \psi \right\rangle$ of an observable $A$ is a measurable quantity associated with an observable $A$ and pre- and post-selected states $\vert\psi \rangle, \vert \phi \rangle$. 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 post- selection 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 set-up.

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