Anomalous Weak Pointer Shifts as Postselected Interference among Coarse-Grained Histories

Abstract:Anomalous weak values and superoscillations allow a pointer to exhibit an effective shift outside the eigenvalue range of the measured observable. We reformulate this effect in a phase-space path-integral language. For each eigenvalue branch $a_j$ of the measured observable, {the interaction couples $a_j$ to the pointer position $\hat{x}_p$ and thereby translates the conjugate pointer momentum by $\gamma a_j$.} After postselection, {the branch-conditioned amplitudes are coherently superposed with coefficients chosen to produce a superoscillatory approximation. When this conditional amplitude acts on an initial pointer momentum wavepacket for which the finite superoscillatory-window condition is satisfied, the resulting momentum wavefunction behaves as if it had been translated by $\gamma A_w$, rather than by any of the eigenvalue-conditioned shifts $\gamma a_j$. This yields an effective path-integral representation of anomalous weak pointer shifts and motivates their interpretation in terms of interference among finite coarse-grained histories.} We discuss how this picture bears on conservation-law questions.

arXiv:2608.15209 [quant-ph]

(or arXiv:2608.15209v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.15209 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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