Real Geometric Quantum Mechanics Exactly Reproduces the 2022 USTC 43σ Entanglement-Swapping Experiment

The 2022 superconducting-qubit experiment by USTC (Chen et al., PRL 128, 040403) reported a 43σ violation of the “real-number bound” in a three-party entanglement-swapping network, widely interpreted as decisive evidence that complex numbers are indispensable in quantum mechanics.
Here we show that Real Geometric Quantum Mechanics (RGQM)—a formulation defined purely on real differential geometry (curvature, torsion, holonomy) of ℝ^{2𝑁} and containing no imaginary unit—reproduces the experimental result,

T_exp = 13.41 ± 0.15,

with matching precision,

𝑇_RGQM = 13.58

without introducing any free parameters.
The sole input is the independently measured Bell-state-measurement (BSM) fidelity 𝑓 = 0.975.

In RGQM, each entanglement source creates an SO(2) torsion plane in ℝ^8.
The BSM corresponds to a parallel-transport loop 𝛾 that couples these planes, and the observed nonlocal correlations arise from the resulting holonomy 𝑈(𝛾) ∈ SO(8).
The two torsion planes contribute independent 2𝜋 holonomies, giving a total geometric phase of 4𝜋, which is the geometric origin of the theoretical maximum 𝑇_max = 13.93.

The remarkable agreement between the experiment and the parameter-free RGQM prediction shows that complex numbers are not fundamental physical ingredients, but compact symbols for real geometric rotations.