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

Shane Mansfield, Tobias Fritz

Research output: Contribution to journalArticlepeer-review


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 occurrence 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.
Original languageEnglish
Pages (from-to)709-719
Number of pages11
JournalFoundations of Physics
Issue number5
Publication statusPublished - 12 Mar 2012


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