Experimental Analysis of a Four-Qubit Photon Cluster State

Linear-optics quantum logic operations enabled the observation of a four-photon cluster state. We prove genuine four-partite entanglement and study its persistency, demonstrating remarkable differences from the usual Greenberger-Horne-Zeilinger (GHZ) state. Efficient analysis tools are introduced in the experiment, which will be of great importance in further studies on multiparticle entangled states.

Figure 1

Experimental setup for the demonstration of the four-photon polarization-entangled cluster state. The state is observed after entangling two EPR pairs via a linear-optics controlled phase gate (C-phase gate), which employs two-photon interference at polarization-dependent beam splitters (PDBS). Two entangled photon pairs are originating from type-II spontaneous parametric down-conversion (SPDC) by pumping a $\beta$-Barium Borate (BBO) crystal in a double pass configuration. Half- and quarter-wave plates (HWP, QWP) together with polarizing beam splitters (PBS) are used for the polarization analysis.

Figure 2

Fourfold coincidence counts obtained during two hours of measurement when analyzing in the $H/V$ basis in all four output modes.

Figure 3

Fourfold coincidence counts obtained during two hours of measurement when analyzing in the $H/V$ basis in modes $a$ and $b$ and in the $\pm 45°$ basis in modes $c$ and $d$ (a), or when analyzing in the $\pm 45°$ basis in modes $a$ and $b$ and in the $H/V$ basis in modes $c$ and $d$ (b), respectively. These data are already sufficient to prove four-photon entanglement based on stabilizer witnesses.

Figure 4

State tomography after projection of photons in mode $b$ and $c$ onto $-45°$. The state $({|H-⟩}_{ad}-{|V+⟩}_{ad})/\sqrt{2})$ is indeed obtained with a fidelity of $0.809\pm 0.027$.