Tomographic test of quantum nonlocality for a time-delocalized single photon

We study the nonlocal nature of a temporally-delocalized single photon by performing the first tomographic test of Bell's inequality. Balanced homodyne detection is performed on two well-separated temporal modes carrying a single photon. The reconstructed two-mode Wigner function is employed to test Bell's inequality in the form theoretically proposed by Banaszek and Wodkiewicz [1]. A clear violation of the predictions of local hidden-variable theories is found, provided some auxiliary assumptions are made. Our experiment is a proof-of-principle demonstration of single-photon nonlocality, and indicates the meaningfulness of extending the concepts of entanglement and nonlocality to a coherently delocalized single photon. Furthermore, we show that the tomographic approach to Bell's inequality may open the way towards completely loophole-free tests of Bell's inequality