We report a quantitative evaluation of weak-value amplification (WVA) for longitudinal phase measurements using Allan variance analysis. Building on a recent double-slit interferometry experiment with real weak values [Phys. Rev. Lett. 134, 080802 (2025)], our Allan variance analysis demonstrates measurement of a few attosecond time delay approaching the shot-noise limit at short averaging intervals of $T=0.01–0.1\mathrm{s}$, representing two orders of magnitude variance reduction compared to the $T=300\mathrm{s}$ operating point in prior implementations. We demonstrate that the Allan-variance noise floor scales with the inverse of the detected photon number $1/N_r$, confirming shot-noise-limited operation with WVA. Furthermore, this $1/N_r$ scaling experimentally validates that WVA can outperform conventional measurement under fixed detected photon number and detector saturation, in the presence of technical noise, as theoretically predicted [Phys. Rev. Lett. 118, 070802 (2017)]. Our results provide rigorous, quantitative evidence of the near-optimal noise performance achievable with WVA, establishing a benchmark for precision optical metrology. This advancement is particularly relevant to applications such as gravitational-wave detection, where signals predominantly occupy the high-frequency regime ($>10\mathrm{Hz}$).

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• Quantum metrology
• Quantum protocols
• Weak values & weak measurements