Hyperentangled Mixed Phased Dicke States: Optical Design and Detection

A recently introduced family of multipartite entangled states, the 4-qubit phased Dicke states, has been created by 2-photon hyperentanglement. Our experimental method allows high state fidelity and generation rate. By introducing quantum noise in the multipartite system in a controlled way, we have tested the robustness of these states. To this purpose the entanglement of the resulting multipartite entangled mixed states has been verified by using a new kind of structural witness.

Figure 1

Generation of the 4-qubit phased Dicke state. (a) Scheme of the entangled 2-photon 4-qubit parametric source that generates the state $|\xi ⟩$. Mirror $M$ reflects both the UV pump beam and the parametric radiation. The lens $L$ is used to obtain parallel modes at the output of the 4-hole screen. HWP (QWP) is an half- (quarter-) wave plate. (b) Optical setup used to transform $|\xi ⟩$ into the state $|D_4^{(\mathrm{ph})}⟩$ and to measure Pauli operators. The phase $\phi$ is used to properly generate $|\xi ⟩$ while ${\phi }_A$ and ${\phi }_B$ are used to measure Pauli path operators for the $A$ and $B$ photon, respectively.

Figure 2

Values of $q_2$ corresponding to different values of the path delay $\Delta x$.

Figure 3

Experimental values of the witness $\overline{\mathcal{W}}$ and the bound on $E_r$ as a function of $q_2$. The curves correspond to the theoretical behavior obtained by setting $q_1=0.05$ and $q_3=0.05$.