Experimental Detection of Multipartite Entanglement using Witness Operators

We present the experimental detection of genuine multipartite entanglement using entanglement witness operators. To this aim, we introduce a canonical way of constructing and decomposing witness operators so that they can be directly implemented with present technology. We apply this method to three- and four-qubit entangled states of polarized photons, giving experimental evidence that the considered states contain true multipartite entanglement.

Figure 1

Experimental setups to demonstrate (a) four-photon entanglement of the ${\Psi }^{(4)}$ state and (b) three-photon entanglement of the $W$ state; (c) polarization analysis (PA) setup.

Figure 2

Three-photon detection probabilities for six settings of the polarization analyzers as required for the detection of three-photon entanglement using the witness operators ${\mathcal{W}}_W^{(1)}$ and ${\mathcal{W}}_W^{(2)}$.

Figure 3

Four-photon detection probabilities for fifteen settings of polarization analyzers as required for the detection of four-photon entanglement using the witness operators ${\mathcal{W}}_{{\Psi }^{(4)}}$.