[en] The theory of a four photon interference experiment is investigated for the testing of the Greenberger-Horne-Zeilinger (GHZ) theorem. The strong correlation in the GHZ theorem is due to the multi-particle Einstein-Podolsky-Rosen type entangled quantum state. We present the theory to construct the four photon EPR state for space-time variables. The four photon nonlocal quantum interference effect itself is also of great interest. (orig.)