Figure 1

Scheme of the experimental setup. (a) The setup to generate the required three-photon GGHZ state, here setting HWP${}_2$ at ${45}^{\circ }$. The entangled photons are generated by pumping the uv laser beam on a BBO crystal and a pseudo-single-photon source is prepared by attenuating the infrared light after the DM. The average power in the experiment is 90 mW and the average twofold coincidence is $6\times {10}^3{\mathrm{s}}^{-1}$ in modes 2 and 3. Prism $\Delta$d1 is used to ensure that the input photons arrive at the PBS${}_{12}$ at the same time. Half-wave plate (HWP) 1 is used to prepare the single-photon state $\frac{1}{\sqrt{2}}{\left(\right|H\rangle }_1+{|V\rangle }_1)$ and HWP${}_2$ is used to prepare the desired two-photon state. To achieve good temporal and spatial overlap at PBS${}_{12}$, every output is spectrally filtered (${\Delta }_{\mathrm{FWHM}}=3\mathrm{nm}$) and monitored by fibre coupled single-photon detectors. Throughout the experiment, the coincidence time window is set to be 5 ns, which ensures that accidental coincidence is negligible. (b) Setup for preparing the MS state. HWP${}_1$ is set at $\pi /8$, and the superposed three-qubit state is GHZ state $\frac{1}{\sqrt{2}}\left(\right|H_1{H}_2{H}_3\rangle +|V_1{V}_2{V}_3\rangle )$. Then we set HWP${}_3$ at $22.5^{\circ }$ and can make the change $|H_3\rangle \to |{+}_3\rangle$, $|V_3\rangle \to |{-}_3\rangle$. This will convert the GHZ state into $\frac{1}{\sqrt{2}}\left(\right|H_1{H}_2{+}_3\rangle +|V_1{V}_2{-}_3\rangle )$. After that we use a polarization dependent beam splitter cube (PBC). Therefore the state is $\frac{1}{\sqrt{2}}\left[\right|H_1{H}_2\rangle \left(a\right|H_3\rangle +b|V_3\rangle )+|V_1{V}_2\rangle \left(a\right|H_3\rangle -b|V_3\rangle )$], then another half-wave plate (HWP${}_4$) setting at an angle chosen according to the transmissions $a$ and $b$ is used behind PBC. Its function is as follows: It changes $a|H_3\rangle +b|V_3\rangle \to |H_3\rangle$, while $a|H_3\rangle -b|V_3\rangle \to \cos {\theta }_3|H_3\rangle +\sin {\theta }_3|V_3\rangle$.Reuse & Permissions

Figure 2

Fidelity of GGHZ states and MS states. The fidelity equals $\langle \psi \left|\rho \right|\psi \rangle$. Each experimental value is obtained by measuring in an average time of 120 seconds. The error bar of the fidelity is calculated by performing a 100 run Monte Carlo simulation of the whole state tomography analysis, with Poissonian noise added to each experimental datum in each run.Reuse & Permissions

Figure 3

Experimental results. The dashed line shows the plot of Eqs. (3) and (4) for $S_{\max }\left({\psi }_g\right)$ versus $\tau$ for the GGHZ states [9]. The labeled lines show the experimental result of Svetlichny inequalities, where the calculation value is calculated from the state density matrix and the measured value is the measured value of the Svetlichny operator.Reuse & Permissions