  It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized
to the case with only two entangled particles. The reasoning makes use of two
photons which are maximally entangled both in polarization and in spatial
degrees of freedom. In contrast to Cabello's argument of "all versus nothing"
nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)], our
proposal to test the theorem can be implemented with linear optics and thus is
well within the reach of current experimental technology.
