Fig. 3: Correlations within rows and columns of the Peres–Mermin square.
From: State-independent test of quantum contextuality with either single photons or coherent light
To characterize the compatibility of different measurement, we switch the orders of the measurements. We take \(\left|{\psi }_{8}\right\rangle =(\left|1\right\rangle +\left|2\right\rangle )/\sqrt{2}\) as an example. We show the measured absolute values of the ensemble average of the products of observables for six possible permutations within rows and columns of the Peres–Mermin square, which fall within the range from 0.957(2) to 0.986(1) and agree with theoretical prediction 1. We find that all values for the non-contextual inequality fall within the range from 5.786(5) to 5.868(4). Even with experimental imperfections, the experimental violation of the non-contextual inequality still agrees with the quantum-mechanical prediction.
