Entanglement probes of gravitational Kaluza-Klein spectra: signal hierarchy and model discrimination

TL;DR

This paper compares three Kaluza-Klein models using quantum entanglement measurements to distinguish their signatures at submillimeter scales, revealing a stable hierarchy and potential for model discrimination.

Contribution

It introduces a comparative analysis of KK spectra via QGEM phase measurements, highlighting their discriminative power at short distances.

Findings

ADD spectrum yields the strongest entanglement signal.

Gapped continuum is resolvable only at the lower end of the distance window.

RSII remains below the resolution threshold in the tested range.

Abstract

Quantum-gravity-induced entanglement of masses (QGEM) provides a phase-sensitive probe of extra-dimensional corrections to the Newtonian potential at submillimeter separations. We compare three representative Kaluza-Klein spectral scenarios: the Randall-Sundrum II (RSII) and Arkani-Hamed-Dimopoulos-Dvali (ADD) models, and the case of a gapped continuum modeled by a P\"oschl-Teller potential. We evaluate the entangling phase, concurrence, and normalized phase-response profiles over $d=40$-$80\,\mu\mathrm{m}$ using representative benchmark parameters guided by current short-range gravity tests. In this range, the signal exhibits a stable hierarchy: ADD $>$ gapped $>$ RSII. For conservative experimental parameters, the ADD signal surpasses the nominal entanglement threshold at smaller separations, whereas the gapped benchmark is resolvable only at the lower end of the window, and RSII remains below resolution. In a more optimistic near-term scenario, all three spectral signatures comfortably exceed the threshold. We further show that normalized distance scans of the phase response clearly separate the RSII benchmark from the ADD and gapped cases, whereas ADD and the gapped continuum remain nearly indistinguishable in normalized profile. QGEM phase observables therefore provide a complementary discriminator of Kaluza-Klein spectral structure at submillimeter scales.