Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair

Abstract

We implemented a joint weak measurement of the trajectories of two photons in a photonic version of Hardy's experiment. The joint weak measurement has been performed via an entangled meter state in polarization degrees of freedom of the two photons. Unlike Hardy's original argument in which the contradiction is inferred by retrodiction, our experiment reveals its paradoxical nature as preposterous values actually read out from the meter. Such a direct observation of a paradox will give us a new insight into the spooky action of quantum mechanics.