Experimental Entanglement and Nonlocality of a Two-Photon Six-Qubit Cluster State

We create a six-qubit linear cluster state by transforming a two-photon hyperentangled state in which three qubits are encoded in each particle, one in the polarization and two in the linear momentum degrees of freedom. For this state, we demonstrate genuine six-qubit entanglement, persistency of entanglement against the loss of qubits, and higher violation than in previous experiments on Bell inequalities of the Mermin type.

Figure 1

Graph associated to a two-photon six-qubit entangled state. Each set represents a photon and each vertex corresponds to a qubit. Each link represents a CZ operation between the two connected qubits. Dashed lines represent links present in the $|{\mathrm{LC}}_6⟩$ state and absent in the $|{\mathrm{HE}}_6⟩$ state. In the experiment, qubits 1 and 4 are encoded into external/internal ($E/I$) modes, qubits 2 and 5 into horizontal/vertical ($H/V$) polarization, and qubits 3 and 6 into right/left ($r/\ell$) modes. See the text for details.

Figure 2

Generation of the six-qubit linear cluster state. (a) Scheme of the entangled two-photon six-qubit parametric source: a UV laser beam (wavelength ${\lambda }_p$) impinges on the Type I BBO crystal after reflection on a small mirror. The polarization entangled state $(|H⟩|H⟩-|V⟩|V⟩)/\sqrt{2}$ arises from the superposition of the degenerate emission cones of the crystal. Basic elements of the source are: (i) A spherical mirror ($M$), reflecting both the parametric radiation and the pump beam, whose micrometric displacement enables phase control between the $|H⟩|H⟩$ and $|V⟩|V⟩$ events. (ii) A quarter wave plate (WP), located between mirror $M$ and BBO, performing the $|H⟩|H⟩\to |V⟩|V⟩$ transformation on the left cone. (iii) A positive lens $L$, transforming the conical parametric emission of the crystal into a cylindrical one. Four pairs of correlated longitudinal modes $a_i-b_i$ ($i=1,\dots ,4$) are selected by an eight-hole screen. One half WP oriented at 45° intercepting modes $a_2$, $a_3$ and two half WPs oriented at 0° intercepting $b_3$, $b_4$ determine the transformation from $|{\widetilde{\mathrm{HE}}}_6⟩$ to $|{\widetilde{\mathrm{LC}}}_6⟩$. (b) Spatial superposition between the left ($\ell$) and right ($r$) modes on the common $50/50$ beam splitter ${\mathrm{BS}}_1$. $\ell$ modes $a_1$, $a_2$ ($b_3$, $b_4$) are respectively matched with $r$ modes $a_4$, $a_3$ ($b_2$, $b_1$) on the $A$ ($B$) side. Temporal indistinguishability is obtained by setting to zero the path delay between the right and the left modes. (c) Spatial superposition between the internal $I$ ($a_2$, $a_3$, $b_2$, $b_3$) and external $E$ ($a_1$, $a_4$, $b_1$, $b_4$) modes is performed on ${\mathrm{BS}}_{2A}$ and ${\mathrm{BS}}_{2B}$ for the $A$ and $B$ photon, respectively. Independent adjustment of time delay between the $A$ and $B$ modes coming out of ${\mathrm{BS}}_1$ determines interference between the modes. After ${\mathrm{BS}}_1$, only the $A$ ($B$) modes contribute to the interference on ${\mathrm{BS}}_{2A}$ (${\mathrm{BS}}_{2B}$), while the others modes are intercepted by beam stops.