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

TL;DR

The paper investigates entanglement in photons produced by para-positronium decay accessed through double Compton scattering, introducing a normalized entanglement witness $O_1$ whose expectation $ abla$ encodes decoherence via a parameter $\\rho$. In the decoherence-free limit $\\langle O_1\\rangle = -1$, while partial decoherence yields $\\langle O_1\\rangle = -(1-\\rho)$, enabling direct experimental quantification of coherence loss. A symmetry-based local-hidden-variable analysis shows that enforcing mirror symmetry in the Compton process imposes a non-negative bound on a key correlation, contradicting the negative QFT prediction for any $0\\le\\rho<1$, thereby excluding symmetry-preserving LHVTs. If the symmetry constraint is relaxed, LHVTs can reproduce the correlations, underscoring the critical role of physical symmetries in testing local realism with quantum electrodynamic processes. The work proposes a practical pathway to test foundational questions using Compton-scattered entangled photons from p-Ps decay and highlights mirror-symmetry as a stringent criterion for ruling out certain LHVT descriptions.

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 $\mathcal{O}_1 = \cos(2φ_1 - 2φ_2)/C_1$ to witness entanglement. In the absence of decoherence, $\langle\mathcal{O}_1\rangle = -1$, corresponding to a maximally entangled Bell state. With decoherence parameterized 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. Imposing the mirror symmetry with respect to the plane defined by the photon spin and momentum leads to a non-negative LHVT prediction for $\langle \sin^2θ_1 \sin^2θ_2 \cos(2φ_1-2φ_2)\rangle$, 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.