Transition between weak and strong measurements in the presence of post-selection
Abstract
In the weak measurement regime, post-selection can result in the observation of anomalous weak values, seemingly contradicting the eigenvalue statistics observed when the measurement interaction is strong. Here, we investigate the dependence of meter statistics on measurement strength in a post-selected measurement. We find that the meter statistics in the intermediate regime between weak and strong measurements is nearly independent of measurement strength and show that, in this regime, the system performs a measurement of momentum on the meter. Our results show that post-selection is extremely sensitive to the action of the meter on the system, highlighting the difference between the weak measurement regime where this back-action is negligible and the average meter position is a valid measurement result, and the intermediate regime where the meter statistics should not be misinterpreted as a measurement outcome. The transition between weak values and eigenvalues is facilitated by a reversal of the roles of the system and the meter, where the post-selection acts as a readout of information about the meter. The intermediate measurement regime thus reveals that the apparent contradictions between anomalous weak values and eigenvalues originate from the non-classical effects of back-action on the post-selected meter statistics.
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BibTeX
@misc{hanashiro2026transition,
title = {{Transition between weak and strong measurements in the presence of post-selection}},
author = {Shogo Hanashiro and Holger F. Hofmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.04812},
eprint = {2609.04812},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04812},
}
RIS
TY - UNPB
TI - Transition between weak and strong measurements in the presence of post-selection
AU - Shogo Hanashiro
AU - Holger F. Hofmann
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2609.04812
UR - https://arxiv.org/abs/2609.04812
AB - In the weak measurement regime, post-selection can result in the observation of anomalous weak values, seemingly contradicting the eigenvalue statistics observed when the measurement interaction is strong. Here, we investigate the dependence of meter statistics on measurement strength in a post-selected measurement. We find that the meter statistics in the intermediate regime between weak and strong measurements is nearly independent of measurement strength and show that, in this regime, the system performs a measurement of momentum on the meter. Our results show that post-selection is extremely sensitive to the action of the meter on the system, highlighting the difference between the weak measurement regime where this back-action is negligible and the average meter position is a valid measurement result, and the intermediate regime where the meter statistics should not be misinterpreted as a measurement outcome. The transition between weak values and eigenvalues is facilitated by a reversal of the roles of the system and the meter, where the post-selection acts as a readout of information about the meter. The intermediate measurement regime thus reveals that the apparent contradictions between anomalous weak values and eigenvalues originate from the non-classical effects of back-action on the post-selected meter statistics.
ER -