Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity

We present the experimental observation of the symmetric four-photon entangled Dicke state with two excitations $|D_4^{(2)}⟩$. A simple experimental setup allowed quantum state tomography yielding a fidelity as high as $0.844\pm 0.008$. We study the entanglement persistency of the state using novel witness operators and focus on the demonstration of a remarkable property: depending on the orientation of a measurement on one photon, the remaining three photons are projected into both inequivalent classes of genuine tripartite entanglement, the Greenberger-Horne-Zeilinger and $W$ class. Furthermore, we discuss possible applications of $|D_4^{(2)}⟩$ in quantum communication.

Figure 1

Experimental setup for the analysis of the four-photon polarization-entangled state $|D_4^{(2)}⟩$, observed after the symmetric distribution of four photons onto the spatial modes $a$, $b$, $c$, and $d$ via nonpolarizing beam splitters.

Figure 2

(a) Real part of the density matrix ${\rho }_{\mathrm{fit}}$ derived from the observed data, (b) density plot of the ideal state ${\rho }_{D_4^{(2)}}$ and, for comparison, (c) the difference between the matrices. Noise on the real and imaginary part is comparable.

Figure 3

Real parts of density matrices for (a) $W$ state after projection of photon $d$ onto $|V⟩$, (b) $G$ state after projection of photon $d$ onto $|-⟩$, (c) residual state after loss of photon $d$. The imaginary parts consist of noise only, comparable to the noise in the real part.