Classical timing noise in gravity-mediated entanglement tests: LOCC structure, metrological bounds, and visibility thresholds

TL;DR

This paper analyzes the impact of classical timing noise on gravity-mediated entanglement experiments, showing it cannot generate entanglement and establishing bounds on its effects relative to local dephasing.

Contribution

It derives the mapping from clock cross-spectra to dephasing rates, proves the LOCC nature of the noise channel, and provides quantitative bounds relevant for experimental proposals.

Findings

Timing noise is a negligible background in entanglement tests.

LOCC channels cannot produce entanglement, limiting the effect of timing noise.

Quantitative bounds on common-mode versus local dephasing ratios across platforms.

Abstract

Table-top proposals to test gravity-mediated entanglement aim to distinguish coherent gravitational interactions from classical dephasing processes that generate identical phases on both interferometers. A particularly important contribution is platform-invariant timing noise, which can be accessed through optical-clock cross-spectra and frequency-transfer links. In this work we (i) derive the mapping from clock cross-spectra to an effective common-mode dephasing rate, (ii) show that the corresponding dynamical channel is LOCC and therefore unable to generate entanglement, and (iii) combine published clock and interferometer noise floors to obtain quantitative bounds on the ratio between common-mode and local dephasing rates in representative gravity-entanglement proposals. Across QGEM-, MAQRO-, and levitated-nanoparticle regimes we find a robust hierarchy $\gamma_{\rm com}/\gamma_{\rm loc}\sim10^{-9}$--$10^{-11}$, identifying platform-invariant timing noise as a negligible but calibratable background. We further derive visibility and Bell--CHSH thresholds in the presence of both common-mode and local dephasing, and illustrate the full calibration workflow with a simple synthetic example anchored to state-of-the-art clock metrology. Extended derivations and statistical tools are provided in the Supplemental Material.