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

2026/08/06 by Holger F. Hofmann, Tomonori Matsushita, Masayoshi Isobe +1
Physics and Astronomy · #quant-ph

paper · pdf

13 pages

arxiv created 2026/08/06 · arxiv updated 2026/08/07

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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