The randomness in 21 quantum random access code without a shared reference frame

The non-classical correlations presented in quantum random access code experiment are a powerful diagnostic tool for semi-device-independent random number generator protocols. The idea behind it is that if the user observes the optimal non-classical correlations, he has the guarantee that the unknown quantum states and measurements in the devices have carefully calibrated (we say have global reference frame), in a relationship which can bring to random outcomes. This means, for observing the non-classical correlations, the devices must have that calibration in previous. However, that calibration can’t always be guaranteed in reality due to unintentional flaws or failures of the quantum apparatuses, thus the devices do not always occur the wanted non-classical correlations. In this paper, we show there will always have non-classical correlations by the proper operations, when the devices have local reference. The quantity of true randomness in the observed non-classical correlations is then quantified by the violation values of some inequality. Besides we also consider the devices without local reference and show the probability of non-classical correlations occurring in 100 trials.