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

Yaghmorassene Hebib

TL;DR

The paper develops an operational framework to separate gravity-mediated quantum entanglement from classical timing noise in tabletop tests. By mapping optical-clock cross-spectra to a common-mode dephasing rate and proving that the corresponding dynamics form an LOCC channel, the authors provide a calibrated, platform-invariant baseline for timing noise. They derive a universal bound γ_com < 10^{-12±1} s^{-1} and show γ_com/γ_loc ≈ 10^{-9}–10^{-11} across QGEM-, MAQRO-, and levitated-nanoparticle platforms, indicating timing noise is a negligible background but a useful calibration handle. A noise-calibrated feasibility inequality for gravity-mediated entanglement is presented, along with an end-to-end example illustrating how clock data constrains visibility analyses. The framework offers a concrete calibration tool for interpreting null results and guiding design choices (mass, separation, and coherence time) to approach the entanglement regime in future experiments.

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 $γ_{\rm com}/γ_{\rm loc}\sim10^{-9}$--$10^{-11}$, 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.

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

TL;DR

The paper develops an operational framework to separate gravity-mediated quantum entanglement from classical timing noise in tabletop tests. By mapping optical-clock cross-spectra to a common-mode dephasing rate and proving that the corresponding dynamics form an LOCC channel, the authors provide a calibrated, platform-invariant baseline for timing noise. They derive a universal bound γ_com < 10^{-12±1} s^{-1} and show γ_com/γ_loc ≈ 10^{-9}–10^{-11} across QGEM-, MAQRO-, and levitated-nanoparticle platforms, indicating timing noise is a negligible background but a useful calibration handle. A noise-calibrated feasibility inequality for gravity-mediated entanglement is presented, along with an end-to-end example illustrating how clock data constrains visibility analyses. The framework offers a concrete calibration tool for interpreting null results and guiding design choices (mass, separation, and coherence time) to approach the entanglement regime in future experiments.

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 --, 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.

Paper Structure

This paper contains 13 sections, 59 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Proper-time fluctuations and common-mode dephasing
  3. LOCC structure of the common-mode timing channel
  4. Metrological bounds from optical-clock cross-spectra
  5. Visibility dynamics and operational thresholds
  6. Analytical Results: Noise-Calibrated Bounds for Gravity-Mediated Entanglement
  7. Discussion: Relation to Previous Approaches and Implications for Future Experiments
  8. Conclusion
  9. Mapping clock cross-spectra to proper-time noise
  10. Filter-function relation and common-mode dephasing rate
  11. LOCC structure of the common-mode sector
  12. Derivation of the CHSH feasibility condition
  13. Details of the feasibility plots and parameter extraction

Figures (1)

  • Figure 1: Feasibility condition for gravitationally mediated entanglement applied to published experimental parameters. Each panel shows the point $(\Gamma_{\phi}t,\chi t)$ evaluated using the parameters listed in Table \ref{['tab:platforms']}, plotted against the visibility threshold $\chi t=\Gamma_{\phi}t+\tfrac{1}{2}\ln(\sqrt{2}/C)$ from Eq. \ref{['eq:feasibility']}. Common-mode gravitational timing noise is fixed by optical-clock limits through Eq. \ref{['eq:gammacom']} and contributes $\gamma_{\rm com}t\lesssim10^{-12}$ across all platforms. QGEM lies closest to the feasibility boundary, with $\chi t\simeq2.5\times10^{-2}$ and $\Gamma_{\phi}t\simeq3\times10^{-3}$. MAQRO, despite extremely low $\gamma_{\rm loc}$, exhibits gravitational phases too small to reach the threshold. Levitated platforms are limited primarily by technical decoherence, yielding $\Gamma_{\phi}t>\chi t$ by several orders of magnitude.