Experimental Evidence for Bounds on Quantum Correlations

We implemented the experiment proposed by Cabello in the preceding Letter to test the bounds of quantum correlation. As expected from the theory we found that, for certain choices of local observables, Tsirelson’s bound of the Clauser-Horne-Shimony-Holt inequality ($2\sqrt{2}$) is not reached by any quantum states.

Figure 1

Experimental setup: The time-compensated source of photon pairs in the state $|\phi (\xi ){⟩}_{ab}$ is composed of a type II nonlinear crystal (NLC2), pumped by the pulsed laser system [GL (green laser), Ti:Sa, and NLC1], of a polarizing beam splitter (PBS), and of half-wave plates (HWP). Photons $a$ and $b$ of each pairs are directed towards the corresponding detection apparatuses ($A$ and $B$) to perform the local measurements, by means of HWPs, dichroic mirrors (DM), fiber couplers, fiber integrated PBS, and single-photon detectors. M, mirror; L, lens.

Figure 2

Plot of the CHSH parameter $S$ versus $\xi$ and $\theta$. “Fig. 3” and “Fig. 4” indicate the projection of the curve $S$ along $\theta$ and $\xi$ directions, respectively.

Figure 3

Experimental data: The CHSH parameter $S$ versus $\xi$. Each curves corresponds to a specific choice of $\theta$. Plot points are the measured values of $S$ for any pair of values $\theta$ and $\xi$.

Figure 4

Experimental data: The CHSH parameter $S$ versus $\theta$. Each curve corresponds to a specific choice of $\xi$. Plot points are the measured values of $S$ for any pair of values $\theta$ and $\xi$.