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arXiv · 1105.1819

Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality

Shane Mansfield·Tobias Fritz
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Abstract

Hardy's non-locality paradox is a proof without inequalities showing that certain non-local correlations violate local realism. It is `possibilistic' in the sense that one only distinguishes between possible outcomes (positive probability) and impossible outcomes (zero probability). Here we show that Hardy's paradox is quite universal: in any (2,2,l) or (2,k,2) Bell scenario, the occurence of Hardy's paradox is a necessary and sufficient condition for possibilistic non-locality. In particular, it subsumes all ladder paradoxes. This universality of Hardy's paradox is not true more generally: we find a new `proof without inequalities' in the (2,3,3) scenario that can witness non-locality even for correlations that do not display the Hardy paradox. We discuss the ramifications of our results for the computational complexity of recognising possibilistic non-locality.

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Shane Mansfield, Tobias Fritz. 2011-05-09. Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality. https://doi.org/10.1007/s10701-012-9640-1

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