  Constraints on the quantum decoherence of entangled $\gamma$ quanta at the
mega-electron-volt scale, such as those produced following positron
annihilation, have remained elusive for many decades. We present the first
statistically and kinematically precise experimental data for triple Compton
scattering of such entangled $\gamma$. An entanglement witness ($R$), relating
to the enhancement of the azimuthal correlation between the final scattering
planes, is obtained where one of the $\gamma$ underwent intermediate Compton
scattering. The measured $R$, deconvolved from multiple scattering backgrounds,
are found to exceed the classical limit for intermediate scatter angles up to
$\sim$60$^{\circ}$ and diminish at larger angles. The data are consistent with
predictions from a first quantum theory of entangled triple Compton scattering
as well as a simple model based approach. The results are crucial to future
study and utilisation of entangled mega-electron-volt $\gamma$ in fundamental
physics and PET imaging.
