Measurement-Device-Independent Entanglement Witness of Tripartite Entangled States and Its Applications

Entanglement witness is of great importance in characterizing quantum systems. The imperfections in conventional entanglement witness schemes could lead to the misidentification of a separated state as an entangled state. Measurement-device-independent entanglement witness (MDIEW) has been proposed and demonstrated to resolve the imperfect measurement devices. So far, however, the MDIEW has been restricted to a two-party qubit entangled state. Here, for the first time, we demonstrate MDIEW for multipartite entangled states. We experimentally detect the genuine entanglement and the entanglement structure of a tripartite entangled state based on an eight-photon interferometry. Furthermore, with the verified multipartite entangled state, we demonstrate quantum randomness generation and open-destination quantum key distribution in an measurement-device-independent manner. Our research presents an important step toward building a robust and secure quantum network.

Figure 1

(a) An illustration of the (a) conventional EW scheme and (b) MDIEW scheme.

Figure 2

A beam of an ultrafast ultraviolet pump laser, which has a central wavelength of 390 nm, a repetition rate of 76 MHz, and a pulse duration of 150 fs, successively passes through four separated BBO crystals. Among these BBO crystals, the second one is a sandwichlike combination of BBO crystals (C-BBO) to generate the entangled pairs $|{\mathrm{\Phi }}^{+}⟩=(|HH⟩+|VV⟩)/\sqrt{2}$ and the other three are the beamlike single BBO crystals to generate correlated photon pairs $|HH⟩$. The photons 2, 3, and 4 are used to prepare the to-be-witnessed state, the photons 1, 5, and 8 are used to prepare the ancillary states randomly chosen by Alice, Bob, and Charlie, and the photons 6 and 7 are used as triggers. At last, the BSMs are performed on photons 1 and 3, 2 and 5, and 4 and 8, respectively. $\mathrm{SC}\text{−}{\mathrm{YVO}}_4$ and $\mathrm{TC}\text{−}{\mathrm{YVO}}_4$ represent spatial compensation (SC) and temporal compensation (TC) ${\mathrm{YVO}}_4$ crystals.

Figure 3

Experimental results of MDIEW. (a) The results of witnessing a Werner-like state ${\rho }_{\mathrm{GHZ}}^v$ with the MDIEW constructed according to $W_I$. The theoretical results ($J_{\text{ideal}}$ blue line) are calculated for the states ${\rho }_{\mathrm{GHZ}}^v$ with different values of $v$ in Eq. (6). The green line is the result calculated with the unideal BSM reconstructed by quantum detector tomography. The $J_{\exp }$ (red point) is the result obtained in our experiment. (b) The results of witnessing a GHZ-like state $|{\mathrm{GHZ}}_{i_1,\dots ,i_m}⟩$ with the MDIEW constructed from $W_{II}^m(\alpha )$. The points in the blue area are genuinely tripartite entangled, in the green area are 2 separable, and in the yellow area are 3 separable. The red diamond, square and triangle represent the experimental results of MDIEW for the state $|{\mathrm{GHZ}}_3⟩$, $|{\mathrm{GHZ}}_{2,1}⟩$ and $|{\mathrm{GHZ}}_{1,1,1}⟩$, respectively.

Figure 4

MDI randomness generated from the outputs for different input settings.