Figure 3

Bell tests requiring no shared reference frame.

Here we perform Bell tests on a two-qubit Bell state, using randomly chosen measurement triads. Thus our experiment requires effectively no common reference frame between Alice and Bob. (a) 100 successive Bell tests; in each iteration, both Alice and Bob use a randomly-chosen measurement triad. For each iteration, the maximal CHSH value is plotted (black points). In all iterations, we get a CHSH violation; the red line indicates the local bound (CHSH = 2). The smallest CHSH value is ~ 2.1, while the mean CHSH value (dashed line) is ~ 2.45. This leads to an estimate of the visibility of , to be compared with 0.913 ± 0.004 obtained by maximum likelihood quantum state tomography²⁸. (See Supplementary Information for further discussion of this slight discrepancy.) Error bars, which are too small to draw, were estimated using a Monte Carlo technique, assuming Poissonian photon statistics. (b) The experiment of (a) is repeated for Bell states with reduced visibility, illustrating the robustness of the scheme. Each point shows the probability of CHSH violation estimated using 100 trials. Uncertainty in probability is estimated as the standard error. Visibility for each point is estimated by maximum-likelihood quantum state tomography, where the error bar is calculated using a Monte Carlo approach, again assuming Poissonian statistics. Red points show data corrected for accidental coincidences (see Methods), the corresponding uncorrected data is shown in blue. The black line shows the theoretical curve from Fig. 2 (inset). Further discussion of the slight discrepancy between experimental and theoretical probabilities of CHSH violation is provided in the Supplementary Information.