 A result due to Colbeck and Renner (2011, 2016), building on work of Branciard et al. (2008), shows that this cannot be done if PI is satisfied. This result has significance both at the operational and the fundamental level. It can be applied at the fundamental level to conclude that any theory with sharper probabilities than the quantum predictions must violate PI. In addition, even if some deterministic theory (such as the de Broglie-Bohm theory) applies at the fundamental level, the Colbeck-Renner theorem can be applied at the operational level, where the probabilities involved may indicate limitations on accessible information about the physical state. A violation of PI at the operational level would permit signalling. Thus, the theorem shows that, as long as the no-signalling condition is satisfied, a would-be eavesdropper attempting to subvert the privacy of a key distribution scheme by intercepting the particle pairs and substituting ones that will yield results that she has some information about, cannot do so without disrupting the correlations between the particle pairs. See Leegwater (2016) for a clear exposition of the theorem.