Experimental Realization of Dicke States of up to Six Qubits for Multiparty Quantum Networking

We report the first experimental generation and characterization of a six-photon Dicke state. The produced state shows a fidelity of $F=0.56\pm 0.02$ with respect to an ideal Dicke state and violates a witness detecting genuine six-qubit entanglement by 4 standard deviations. We confirm characteristic Dicke properties of our resource and demonstrate its versatility by projecting out four- and five-photon Dicke states, as well as four-photon Greenberger-Horne-Zeilinger and $W$ states. We also show that Dicke states have interesting applications in multiparty quantum networking protocols such as open-destination teleportation, telecloning, and quantum secret sharing.

Figure 1

(a) Setup for generating the six-photon Dicke state $|D_6^{(3)}⟩$. Photons are distributed into modes 1,…,6 via a 1-to-3 fiber coupler, followed by $50:50$ BSs. The expected probability to find one photon in each spatial mode, corresponding to the state $|D_6^{(3)}⟩$, is $p\sim 0.015$. The fiber and BSs introduce birefringence, compensated by fiber-squeezers and birefringent crystals. State characterization is performed via polarization analysis of sixfold coincidences by a quarter-wave plate (QWP), a half-wave plate (HWP), and a polarizing beam splitter (PBS), whose output ports are monitored by multimode fiber-coupled single-photon detectors. Each detector signal enters a coincidence logic that records multiphoton coincidences. (b) Biseparability region (shaded) for $⟨{\mathcal{W}}^s(\alpha ){⟩}_{bs}$ and experimental point (predicted line) for $⟨{\mathcal{W}}^s(\alpha ){⟩}_{{\varrho }_6^{(3)}}$.

Figure 2

Experimental study of the six-photon Dicke state ${\rho }_6^{(3)}$. (a)–(c) Correlations $⟨{\sigma }_i^{(j)}{\sigma }_i^{(k)}⟩$ for qubit pairs ($j$, $k$) ($i=x$, $y$, $z$) for $⟨{\mathcal{W}}^s(\alpha )⟩$. Dashed lines are ideal values. (d), (e), and (g) Coincidences for photons measured in $|\pm ⟩=(|H⟩\pm |V⟩)/\sqrt{2}$, $|L\mathrm{\text{or}}R⟩=(|H⟩\pm i|V⟩)/\sqrt{2}$, and $|H\mathrm{\text{or}}V⟩$ (rescaled). (f) Ideal populations for (d) and (e). (h) and (i) Multiphoton correlations. Dashed (solid) lines are the patterns of $⟨{\mathcal{C}}_{x/y,z}^{\otimes 6}(\theta )⟩$ for $|D_6^{(3)}⟩$ (${\rho }_{\mathrm{sim}}$). The dots are experimental points.

Figure 3

Experimental data for the Dicke states ${\varrho }_5^{(2)}$ and ${\varrho }_4^{(2)}$. (a) and (b) [(g) and (h)] Correlations $⟨{\sigma }_i^{(j)}{\sigma }_i^{(k)}⟩$ for qubit pairs ($j$, $k$) of ${\varrho }_5^{(2)}$ (${\varrho }_4^{(2)}$), with $i=x$, $y$. (c)–(e) [(i)–(k)] Coincidences for the five (four) photons measured in $|H\mathrm{\text{or}}V⟩$, $|\pm ⟩$, and $|L\mathrm{\text{or}}R⟩$. (f) [(l)] Ideal populations for $|\pm ⟩$ and $|L\mathrm{\text{or}}R⟩$. (m) Navigating the Dicke class by measurement.

Figure 4

Experimental data for the $W$ state ${\varrho }_4^{(1)}$. (a)–(c) Coincidence counts for ${\varrho }_4^{(1)}$ in the rescaled $|H/V⟩$, $|\pm ⟩$, and $|L/R⟩$ bases. (d) Ideal populations for (b) and (c). (e) Maximum achievable fidelity $F_{\max }$ using pair ($i$, $j$) as a channel. The upper (lower) line shows the ideal (classical) value.