Experimental Entanglement of a Six-Photon Symmetric Dicke State

We report on the experimental observation and characterization of a six-photon entangled Dicke state. We obtain a fidelity as high as $0.654\pm 0.024$ and prove genuine six-photon entanglement by, amongst others, a two-setting witness yielding $-0.422\pm 0.148$. This state has remarkable properties; e.g., it allows obtaining inequivalent entangled states of a lower qubit number via projective measurements, and it possesses a high entanglement persistency against qubit loss. We characterize the properties of the six-photon Dicke state experimentally by detecting and analyzing the entanglement of a variety of multipartite entangled states.

Figure 1

Schematic experimental setup for the observation of the Dicke state $|D_6^{(3)}⟩$. SPDC photons generated in the 1 mm thick $\beta$-barium borate (BBO) crystal inside the UV-enhancement cavity pass a half-wave plate (HWP) and a 0.5 mm thick BBO crystal to compensate beam walk-off effects. Their spatial mode is defined by coupling into a single-mode (SM) fiber. Spectral selection is achieved by a band-pass filter (RG) and a 3 nm interference filter (IF) at 780 nm. Birefringence of beam splitters ${\mathrm{BS}}_1–{\mathrm{BS}}_5$ (${\mathrm{BS}}_1–{\mathrm{BS}}_4$ have a splitting ratio of $0.58:0.42$ and ${\mathrm{BS}}_5$ of $0.52:0.48$) is compensated for by pairs of birefringent Yttrium-vanadate (${\mathrm{YVO}}_4$) crystals in the six output modes $a$, $b$, $c$, $d$, $e$, $f$. Polarization analysis (${\mathrm{PA}}_j$) in each mode is performed via a HWP and a quarter-wave plate (QWP) in front of a polarizing beam splitter (PBS). The photons are detected by single-photon avalanche photodiodes (APDs). The detection signals of the 12 detectors are fed into a FPGA controlled coincidence logic allowing histograming of the $2^{12}$ possible detection events between the 12 detectors.

Figure 2

Experimentally measured coincidences for the bases (a) $z$, (b) $x$, and (c) $y$ with eigenvectors $|H\mathrm{\text{or}}V⟩$, $|\pm ⟩$, and $|L\mathrm{\text{or}}R⟩$, respectively. Theoretical predictions are shown as pale gray bars normalized to the total number of coincidences. The insets in (b) and (c) are magnified views of a part of all coincidences, where for clarity expected counts are shown next to experimental ones.

Figure 3

Experimentally measured coincidence counts in the $z$ basis [(a)–(e)] and $x$ basis (f) for projections of $|D_6^{(3)}⟩$ to obtain (a)–(b) five- and (d)–(f) four-qubit entangled states. (c) ${\rho }_5$ obtained after a loss of a qubit from $|D_6^{(3)}⟩$. Each measurement took 279 min. Theoretical predictions are shown as pale gray bars normalized to the total number of coincidences.

Figure 4

Experimental results [dark gray (blue)] and theoretical predictions (pale gray) are shown for the various entanglement witnesses for different states (see text). Negative values prove genuine $N$-partite entanglement.