It's well known that quantum entangled systems can exhibit correlations that go beyond those that could be seen if Nature worked in intuitive “classical” ways. However, as Richard Feynman noted, classical theory can support exhibiting such correlations if we invoke *negative* probabilities to describe their properties. What he did not do was specify how these negative probabilities ought to be chosen, and without any justification, an infinite number of different combinations could be chosen that will satisfy the relevant equations.

The concept of negative probabilities seems nonsensical because they cannot actually be observed—indeed, they cannot be observed even within the framework of quantum theory due to the effects of measurement back-action. Here, we show how they can instead be inferred through the use of *weak measurements*, where a meter is only weakly coupled to the property of interest, thereby avoiding the back-action problem. Each individual weak measurement has a …