In 2022, physicists observed gravity shifting the phase of a single atom's wave, the gravitational analog of the Aharonov–Bohm effect. This experiment became part of a long-standing debate: whether gravity must be quantized or remains a classical background in the quantum world. The direct path to an answer is to entangle two massive particles purely through gravity. Such gravitationally mediated entanglement (quantum correlation between particles due to gravity) is an elusive bridge between a single particle and a pair of particles. Building this bridge in the lab has so far been impossible: you need to hold two particles in superposition at a significant distance simultaneously. But new work shows that the bridge can be built from one shore: it suffices to test the Schrödinger equation for a single particle in the field of an external mass.

The idea is framed in the language of quantum channels. The unknown time evolution is modeled as a linear map that takes density matrices to density matrices; only positivity (or complete positivity) of this map is required. Two assumptions link the single-particle test to entanglement of two: symmetry of the evolution under particle exchange (analogous to Newton's third law) or dependence of the interaction only on the product of masses (a consequence of the equivalence principle). The analytical proof uses the Choi matrix (a table that fully describes a quantum channel), while the numerical one uses semidefinite programming with 1000 random states. Key parameters are taken from realistic proposals: a cesium atom, a 10 kg tungsten sphere at a distance of 3 mm, and an interaction time of 1 s.

The result is two theorems. The first, qualitative: if the Schrödinger equation holds exactly for a single delocalized particle in the field of a 20 g mass, and the evolution is completely positive and symmetric, then gravitationally mediated entanglement is inevitable. The second, quantitative: if the evolution is merely positive and depends only on the product of masses, then it suffices to bound decoherence from above by λ₀ ≈ 0.9995 to guarantee entanglement. Modern interferometers have phase sensitivity around 50 μrad, which corresponds to a measurement precision of λ₀ better than 1.6·10⁻⁴, which is sufficient. Numerical analysis shows that the minimum eigenvalue of the partially transposed density matrix becomes negative at λ₀ ≥ 0.9995, which signals entanglement.

The work moves the problem from the experimental to the theoretical plane: there is no need to wait for the construction of complex setups, just to interpret data from existing atom interferometers. This sets it apart from neighboring works that either propose specific GME schemes or discuss whether classical gravity can entangle. Here it is shown for the first time that testing the Schrödinger equation for a single particle under minimal assumptions yields a rigorous proof of the existence of GME. The main conclusion: the bottleneck is not technique but the lack of consensus on what observing entanglement means for the quantum nature of gravity.

The immediate task is to clarify the exact implications of the existence of GME. It will be necessary to reconcile relativistic locality from quantum field theory with the locality of subsystems from quantum information, possibly within generalized probabilistic theories. An open question is whether the assumptions can be relaxed: can we drop symmetry or dependence on the product of masses? It is also unclear whether requiring only positivity of the evolution is sufficient, or whether complete positivity is justified in the nonrelativistic regime. These questions may be addressed within the program of axiomatizing quantum theory. The bridge, built from one shore, now awaits those who dare to cross it.