  An experiment for the advanced undergraduate laboratory which allows students
to study the effect of photon polarisation in Compton scattering and to explore
q\ uantum entanglement is described. The quantum entangled photons are produced
through electron-positron annihilation in the $S$-state, and their
polarisations a\ re analysed using the Compton scattering cross-section
dependence on the photon polarisation. The equipment necessary for this
experiment is available at a typ\ ical undergraduate physics laboratory. Finite
geometry effects are discussed and investigated with the use of a Geant4-based
simulation.
