Experimental Realization of a Three-Qubit Entangled $W$ State

We report on the experimental observation of the three-photon polarization-entangled $W$ state using spontaneous parametric down-conversion. This state is inequivalent to the Greenberger-Horne-Zeilinger state under stochastic local operations and classical communications and thus is the representative of the second class of genuine tripartite entanglement. We study the characteristic features of entanglement and demonstrate the high degree of two-photon entanglement in the $W$ state.

Figure 1

Experimental setup for the demonstration of the three-photon polarization-entangled $W$ state. For details, see text.

Figure 2

Threefold coincidence probabilities measured (a) in the $H/V$ basis showing the three term structure of a $W$ state, and (b) in the $L/R$ basis verifying the superposition of the three terms. (c) Three photon polarization correlation with fixed settings ${\varphi }_b={\varphi }_c=0$ (filled circles) and ${\varphi }_b=\pi /2$, ${\varphi }_c=0$ (open circles) showing a visibility $\mathcal{V}$ of $0.864\pm 0.019$ and $0.481\pm 0.029$, respectively.

Figure 3

Correlations between photons in modes $a$ and $b$, conditioned on the detection of a $H$-polarized photon (filled circles) or the detection of a $V$-polarized photon (open circles) in mode $c$.

Figure 4

Real parts of experimentally determined density matrices of the two photons in modes $a$ and $b$, conditioned on the detection of a (a) $H$-polarized photon or (b) $V$-polarized photon in mode $c$.