Can Mirror Symmetry Challenge Local Realism? Probing Photon Entanglement from Positronium via Compton Scattering

Abstract

This study investigates photon entanglement generated from para-positronium decay by analyzing azimuthal correlations after the double Compton scattering with stationary electrons. We introduce a normalized correlation observable ${\mathcal{O}}_1=\cos (2{\varphi }_1-2{\varphi }_2)/C_1$ to witness entanglement. In the absence of decoherence, $⟨{\mathcal{O}}_1⟩=-1$, corresponding to a maximally entangled Bell state. With decoherence parameterized by $\rho$, the expectation becomes $-(1-\rho )$, 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. Imposing the mirror symmetry with respect to the plane defined by the photon spin and momentum leads to a non-negative LHVT prediction for $⟨{\sin }^2{\theta }_1{\sin }^2{\theta }_2\cos (2{\varphi }_1-2{\varphi }_2)⟩$, contradicting the negative QFT prediction value for any $\rho <1$. 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.

Comments: 16 pages