The collapse time of weak measurement on N entangled sites
Abstract
We determine the time required for local weak measurements to collapse to one occupied site in an initial superposition of N alternatives in the model of PRA 111, 032217 (2025). For equal initial occupation probabilities and a fixed confidence threshold 1−δ, we prove TN/ln N→1/2 in L1, with time measured in units of the characteristic measurement time τm of each detector. We also connect the asymptotic stabilization theorem of that work to a finite measurement: the first site to reach 1−δ is the eventual outcome with conditional probability exactly 1−δ. The result corrects the previously proposed double-logarithmic asymptotic scaling. The finite-range numerical fit does not determine a constant asymptotic correction or a precise finite-N law.
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BibTeX
@misc{van2026collapse,
title = {{The collapse time of weak measurement on $N$ entangled sites}},
author = {Truong-Son P. Van and David W. Snoke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04556},
eprint = {2610.04556},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04556},
}
RIS
TY - UNPB
TI - The collapse time of weak measurement on N entangled sites
AU - Truong-Son P. Van
AU - David W. Snoke
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04556
UR - https://arxiv.org/abs/2610.04556
AB - We determine the time required for local weak measurements to collapse to one occupied site in an initial superposition of N alternatives in the model of PRA 111, 032217 (2025). For equal initial occupation probabilities and a fixed confidence threshold 1−δ, we prove T_N/ln N→1/2 in L^1, with time measured in units of the characteristic measurement time τ_m of each detector. We also connect the asymptotic stabilization theorem of that work to a finite measurement: the first site to reach 1−δ is the eventual outcome with conditional probability exactly 1−δ. The result corrects the previously proposed double-logarithmic asymptotic scaling. The finite-range numerical fit does not determine a constant asymptotic correction or a precise finite-N law.
ER -