Various quantum nonlocality tests with a commercial two-photon entanglement source

Nonlocality is a fascinating and counterintuitive aspect of nature, revealed by the violation of a Bell inequality. The standard and easiest configuration in which Bell inequalities can be measured has been proposed by Clauser-Horne-Shimony-Holt (CHSH). However, alternative nonlocality tests can also be carried out. In particular, Bell inequalities requiring multiple measurement settings can provide deeper fundamental insights about quantum nonlocality, as well as offering advantages in the presence of noise and detection inefficiency. In this paper we show how these nonlocality tests can be performed using a commercially available source of entangled photon pairs. We report the violation of a series of these nonlocality tests ($I_{3322}$, $I_{4422}$, and chained inequalities). With the violation of the chained inequality with 4 settings per side we put an upper limit at 0.49 on the local content of the states prepared by the source (instead of 0.63 attainable with CHSH). We also quantify the amount of true randomness that has been created during our experiment (assuming fair sampling of the detected events).

Figure 1

Nonlocality tests where Alice and Bob measure the $N$ binary operators {$A_1,\dots ,A_N$} and {$B_1,\dots ,B_N$}, respectively, on the photon pairs produced by the entanglement source in the middle.

Figure 2

Simple sketch of the polarization entanglement source. Linear polarizers at the Alice and Bob site are used for the settings necessary for the measurement of the Bell inequalities.

Figure 3

Largest local part associated with a Werner state for $V=1$, 0.98, 0.96, 0.94, and 0.92 (from bottom to top).

Figure 4

Largest local part as a function of the number of settings per side. The red line joins the expected values for our state. The minimum measured value of $p_L^{\max }$ is $0.491\pm 0.012$ with a chained inequality of $4$ settings per side.

Figure 5

Upper bound on the marginal probability distribution as a function of the inequalities violation. The bound implied by the no-signaling principle is identical for all chained inequalities.