Hardy's paradox for multi-settings and high-dimensional systems

Abstract

Recently, Chen et al introduced an alternative form of Hardy's paradox for $2$-settings and high-dimensional systems [Phy. Rev. A 88, 062116 (2013)], in which there is a great progress in improving the maximum probability of the nonlocal event. Here, we construct a general Hardy's paradox for multi-settings and high-dimensional systems, which (i) includes the paradox in [Phy. Rev. A 88, 062116 (2013)] as a special case, (ii) for spin-1/2 systems, is equivalent to the ladder proof of nonlocality without inequalities in [Phy. Rev. Lett. 13, 2755 (1997)], (iii) for spin-1 systems, increases the maximum probability of the nonlocal event by adding the number of settings, specially, with only 5-settings it can be improved to 0.40184, which is more than two times higher than 0.171, the maximal success probability to prove nonlocality in Adan's paradox [Phy. Rev. A 58, 1687 (1998)].

arXiv comment7 pages

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• Increased success probability in Hardy's nonlocality: Theory and demonstration
• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
• Orthogonal product sets with strong quantum nonlocality on plane structure
• Orbital-angular-momentum-based experimental test of Hardy's paradox for multisetting and multidimensional systems
• Strong quantum nonlocality with genuine entanglement in an $N$-qutrit system
• On Possibilistic Conditions to Contextuality and Nonlocality
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• A Logical Proof of Quantum Correlations Requiring Entanglement Measurements
• Strongest quantum nonlocality in $N$-partite systems
• Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario