All-Versus-Nothing Nonlocality Test of Quantum Mechanics by Two-Photon Hyperentanglement

We report the experimental realization and the characterization of polarization and momentum hyperentangled two-photon states, generated by a new parametric source of correlated photon pairs. By adoption of these states an ”all-versus-nothing” test of quantum mechanics was performed. The two-photon hyperentangled states are expected to find at an increasing rate a widespread application in state engineering and quantum information.

Figure 1

(a) Parametric source of polarization-momentum hyperentangled two-photon states. Phase setting $\theta =0,\pi$ and $\phi =0,\pi$ are obtained by micrometric translation of the spherical back mirror and by tilting of the glass plate on mode $a_1$; (b) spatial coupling of input modes $a_1-b_1$, $a_2-b_2$ on the $BS$ plane. The $BS$ output modes, $a_1^{\prime }-b_1^{\prime }$, $a_2^{\prime }-b_2^{\prime }$, are also shown. $M_1$ and $M_2$ are mirrors inserted to separate upper and lower modes; (c) coincidence rate $C(a_1^{\prime },b_1^{\prime })$ vs $\Delta x$: $\theta =0$, $\varphi =0$ (upper curve), $\theta =0$, $\varphi =\pi$ (lower curve).

Figure 2

Experimental apparatus to measure the expectation values of the nine operators comparing in $\mathcal{O}$. (a) Modes $a_1,b_1$, $a_2$, and $b_2$, separated by the pickoff mirrors $M_1$ and $M_2$, are directly coupled to detectors; polarization analysis is performed in the orthonormal bases, either $H-V$ or $D-\overline{D}$, by rotating the half-wave plates $HW$ before the detectors. The half-wave plate $H{W}^{*}$ performing the $|\Phi ⟩\to |\Psi ⟩$ transformation is also shown. By this configuration one can evaluate the values of $z_1·z_2$, $x_1·x_2$, $z_1^{\prime }·z_2^{\prime },z_1{z}_1^{\prime }·z_2·z_2^{\prime }$, and $x_1·z_1^{\prime }·x_2{z}_2^{\prime }$. (b) The two mode sets $a_1-b_1$ and $a_2-b_2$ are spatially combined onto the $BS$ before being coupled to detectors. In this way one can perform the transformation on the momentum basis, and measure the values of $x_1^{\prime }·x_2^{\prime }$, $x_1{x}_1^{\prime }·x_2·x_2^{\prime }$, and $z_1·x_1^{\prime }·z_2{x}_2^{\prime }$. The same apparatus is used for performing the Bell state analysis by removing $H{W}^{*}$ plate, in order to evaluate the value of $z_1{z}_1^{\prime }·x_1{x}_1^{\prime }·z_2{x}_2^{\prime }·x_2{z}_2^{\prime }$.

Figure 3

Barchart of expectation values for the nine operators involved in the experiment. The following results have been obtained: $z_1·z_2=-0.9428\pm 0.0030$, $z_1^{\prime }·z_2^{\prime }=-0.9953\pm 0.0033$, $z_1{z}_1^{\prime }·z_2·z_2^{\prime }=0.9424\pm 0.0030$, $x_1·x_2=-0.9215\pm 0.0033$, $x_1·z_1^{\prime }·x_2{z}_2^{\prime }=0.9217\pm 0.0033$, $x_1^{\prime }·x_2^{\prime }=-0.8642\pm 0.0043$ $z_1·x_1^{\prime }·z_2{x}_2^{\prime }=0.8039\pm 0.0040$, $x_1{x}_1^{\prime }·x_2·x_2^{\prime }=0.8542\pm 0.0040$, $z_1{z}_1^{\prime }·x_1{x}_1^{\prime }·z_2{x}_2^{\prime }·x_2{z}_2^{\prime }=-0.8678\pm 0.0043$.