 Hardy's paradox

A two-setting nonlocality argument in which several zero-probability events forbid a further coincidence in any deterministic local hidden-variable model, but quantum theory assigns that coincidence positive probability. For binary indicators, suppose $C_{+}^R{C}_{-}^R=0$, $D_{+}^I=1\Rightarrow C_{-}^R=1$ and $D_{-}^I=1\Rightarrow C_{+}^R=1$. Any assignment with $D_{+}^I{D}_{-}^I=1$ would violate the first relation. A quantum implementation can nevertheless give such a coincidence. Real imperfect experiments require an inequality that accounts for their nonzero error probabilities. Lucien Hardy gave a two-particle inequality-free argument in 1992.^[ref]