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arXiv · 2608.05494

What meter interference can tell us about the statistics of weak measurements

Holger F. Hofmann·Tomonori Matsushita·Masayoshi Isobe·Jonte R. Hance
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Abstract

It is widely assumed that the quantum fluctuations of the meter readout in a weak measurement make it impossible to identify the contributions originating from the individual values of the physical property observed in the measurement. Here, we show that a careful analysis of the quantum dynamics of the meter system allows us to identify a universal relation between quantum interference in the post-selection probability, and quantum interference in the statistics of the meter readout. The analysis reveals that quantum interference modifies the readout distribution of the meter in two ways, a diffusion term that identifies the appropriate operator ordering in the post-selected variance of the observed system property, and a wavefunction-dependent update of the initial meter statistics based on the effect of back action on the post-selection probability. Our results show that the statistical patterns described by meter interference provide important details about the physics of post-selection in weak measurements, allowing us to exclude the possibility of statistical artefacts in the experimental observation of weak values.

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Holger F. Hofmann, Tomonori Matsushita, Masayoshi Isobe, Jonte R. Hance. 2026-08-06. What meter interference can tell us about the statistics of weak measurements. https://arxiv.org/abs/2608.05494

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