Polarization Correlations of Entangled Photon Pairs from Positronium Decay as a Test of Bell's Inequality

Matej Peranić, Martin Lončarić, Anton Radman +1 more

Akio Yoshizawa, Hidemi Tsuchida

Ting Zhou

Conventional tests of Bell’s inequality rely on entangled photon pairs. Here, we replace entangled pairs with two independent photons of orthogonal polarization, and demonstrate that Bell’s inequality is still violated. Given the inherent local realism of independent photons, this experiment proves that Bell’s inequality cannot falsify the local realism of photons. We thus conjecture that the violation of Bell’s inequality by entangled photon pairs originates from their orthogonal polarizations, rather than the breakdown of local realism. To interpret this unexpected violation with independent photons, we further substitute the two photons with two monochromatic light beams, and calculate the transmittance correlation through polarizers via Malus’s law and Karl Pearson’s correlation formula. We show that this correlation also defies Bell’s inequality. Retracing the derivation of Bell’s inequality reveals its validity is restricted to binary events, which accounts for the observed violation with light beams. Finally, we propose a thought experiment involving gradual attenuation of light intensity down to the single-photon regime, and hypothesize that single-photon transmission through a polarizer does not constitute a binary event. This hypothesis provides a unified interpretation for both our experimental findings and all canonical Bell inequality tests reported to date.

Herbert Karl Dreiner

In this talk given at the TAU92 Workshop, Columbus, OH, Sept. 92, we summarize results presented in more detail in a recent paper by S. Abel, M. Dittmar and the author where we gave a general proof that Bell's inequality can not be tested at a collider experiment. In particular, a measurement of correlated tau-spins at LEP does not constitute a test of local realistic theories via Bell's inequality. The central point of the argument is that such tests, where the spins of two particles are inferred from a scattering distribution, can always be described by a local hidden variable theory. In response to questions at the workshop we go beyond the paper and show that an old experiment involving the measurement of the correlated spins of the two photons emitted in positronium decay via Compton-scattering is also not a viable test of Bell's inequality.

Paul Joos, Peter Kling

Electron and positron can form a meta-stable bound state called positronium that decays via pair annihilation. We show how polarization-dependent Compton scattering can be used to verify that the two annihilation photons in the spin-zero case (para-positronium) are emitted in a maximally entangled Bell state. Our theoretical approach based on two-photon density matrices connects concepts from relativistic quantum electrodynamics and quantum information theory.

Frederick M. Kronz