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Entanglement of annihilation photons

We present a new experimental study of the quantum entanglement of photon pairs produced in positron-electron annihilation at rest. Each annihilation photon has an energy that is ﬁve orders of magnitude higher than the energy of photons in optical experiments, which provides a unique opportunity for controlled formation of decoherent states and successive measurements of the same photon.The experimental setup includes a system of Compton polarimeters to measure the Compton scattering of annihilation photons in entangled and decoherent states. Decoherent states are prepared by pre-scattering of one of the initial photons prior to measurements in polarimeters. For the ﬁrst time, a direct comparison of the polarization correlations of annihilation photons in the entangled and thus prepared separable states has been carried out. The angular distributions of scattered photons turned out to be the same in both quantum states, which is an unexpected discovery for the quantum-entangled positron emission tomography. Moreover, the correlation function in the Bell’s inequality is also the same for entangled and separable states. It follows that, despite numerous measurements in a series of experiments, there is still no experimental proof of the entanglement of annihilation photons. These results are in line with recent theoretical predictions of an identical Compton scattering cross-section for entangled and speciﬁc mixed separable quantum states and cast doubt on the universality of the Bell’s theorem for testing the entanglement and nonlocality in quantum theory.