Published in Physical Review A: Using weak values to experimentally determine “negative probabilities” in a two-photon state with Bell correlations

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 high uncertainty, but by measuring many instances of a larger ensemble, an average can be found that implies a specific set of anomalous (i.e. beyond 0–1) probabilities. With an experimental demonstration, we thus give an empirically justified method for choosing the anomalous probabilities that allow the classical model to exhibit quantum correlations.

B. L. Higgins, M. S. Palsson, G. Y. Xiang, H. M. Wiseman, and G. J. Pryde
Phys. Rev. A 91, 012113 (2015)

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