Can mirror symmetry challenge local realism? Probing photon entanglement from positronium via Compton scattering

This study investigates photon entanglement generated from parapositronium decay by analyzing azimuthal correlations after the double Compton scattering with stationary electrons. We introduce a normalized correlation observable O 1 = cos ( 2 ϕ 1 − 2 ϕ 2 ) / C 1 to witness entanglement. In the absence of decoherence, ⟨ O 1 ⟩ = − 1 , corresponding to a maximally entangled Bell state. With decoherence parametrized by ρ , the expectation becomes − ( 1 − ρ ) , allowing direct experimental quantification of coherence loss. A prior symmetry analysis of the Compton scattering process within the quantum field theory (QFT) is provided, which establishes the mirror-symmetric nature of the single-photon angular distribution. We further examine a local hidden-variable theory (LHVT) under the angular-momentum conservation and the rotation invariance. Imposing the mirror symmetry with respect to the plane defined by the photon spin and momentum leads to a non-negative LHVT prediction for ⟨ sin 2 θ 1 sin 2 θ 2 cos ( 2 ϕ 1 − 2 ϕ 2 ) ⟩ , contradicting the negative QFT prediction value for any ρ < 1 . Thus, mirror symmetry serves as a novel criterion to exclude LHVT descriptions of the entangled state, whereas without preserving this symmetry, LHVTs can reproduce the correlations.