Figure 1

Experimental setups. (a) An ultraviolet beam from Argon ion laser (351.1 nm, 120 mW) is directed into the BBO crystal from opposite directions, and thus can create photon pairs (with wavelength 702.2 nm) in $|\Psi ⟩$. Four compensators (Comp.) are used to offset the birefringent effect caused by the BBO crystal during parametric down-conversion. The reflection mirrors M0 and M1 are mounted on translation stages, to balance each arm of the interferometer and to optimize the entanglement in path. (b) Apparatuses to measure all necessary observables of doubly entangled states. $D$ is single-photon count module, with collection and detection efficiency 26%; IF is interference filter with a bandwidth of 2.88 nm and a center wavelength of 702.2 nm; Pol. is polarizer. Apparatus $c$ has been included in (a) at the locations of Alice and Bob.Reuse & Permissions

Figure 2

Interference fringe observed when M0 being moved to achieve perfect temporal overlap and to adjust the phase $\varphi =0$. (a), (b) Observed interference fringe for roughly achieving the temporal overlap of modes $R_A$ and $L_A$ and of modes $R_B$ and $L_B$. We measure the twofold coincidence between the output modes toward detectors ${\mathrm{D}}_{A2}$ and ${\mathrm{D}}_{B2}$ behind 45° polarizers, by scanning the positions of M0 (a) and of M1 (b). The envelope of the observed twofold coincidence varies indicating the visibility of the two-photon interference. Inside the coherent region, the best visibility is obtained at the position where perfect temporal overlap is achieved. We perform fine adjustment of the position of M1 and repeat the scanning of M0 until the best visibility is obtained. Note that the ranges of the two envelopes (a) and (b) correspond to the two- and single-photon coherence lengths, respectively. (c) We use a piezotranslation stage to move the mirror M0 to perform a fine scan around the center of the envelope. By setting the piezosystem to a position where we observe maximum twofold coincidence of ${\mathrm{D}}_{A2}\mathrm{\text{−}}{\mathrm{D}}_{B2}$, we then achieve $\varphi =0$.Reuse & Permissions

Figure 3

Predictions of LR (a) and of QM (b), and observed results (c) for the $z_A{z}_A^{\prime }·x_A{x}_A^{\prime }·z_B{x}_B^{\prime }·x_B{z}_B^{\prime }$ experiment.Reuse & Permissions