发表机构
Ho Chi Minh City University of Technology, Vietnam National University; University of Pittsburgh（胡志明市理工大学，越南国立大学; 匹兹堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究 $N$ 个纠缠位点弱测量的坍缩时间，证明在置信阈值 $1-\delta$ 下 $T_N/\ln N \to 1/2$，并修正了双对数渐近标度。
AI 中文摘要
我们确定了在 PRA 111, 032217 (2025) 的模型中，初始叠加态包含 $N$ 个备选位点时，局部弱测量坍缩到一个占据位点所需的时间。对于相等的初始占据概率和固定的置信阈值 $1-\delta$，我们证明了在 $L^1$ 意义下 $T_N/\ln N \to 1/2$，其中时间以每个探测器的特征测量时间 $\tau_m$ 为单位。我们还将该工作中的渐近稳定化定理与有限测量联系起来：第一个达到 $1-\delta$ 的位点即为最终结果，其条件概率恰好为 $1-\delta$。该结果修正了先前提出的双对数渐近标度。有限范围的数值拟合无法确定常数渐近修正或精确的有限 $N$ 定律。
英文摘要
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 $T_N/\ln N\to1/2$ 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.
Comments21 pages, 1 figure
