Realigned Hardy’s paradox

Abstract

Hardy’s paradox provides an “All-versus-Nothing” fashion to directly certify that quantum mechanics cannot be completely described by local realistic theory. However, when considering potential imperfections in experiments, like noisy entanglement source and low detection efficiency, the original Hardy’s paradox can only induce a rather small Hardy violation, and is difficult to reveal. To overcome this challenge, we have proposed a realigned Hardy’s paradox, which can dramatically improve the Hardy violation. Furthermore, we have generalized the realigned Hardy’s paradox to arbitrary even n dichotomic measurements. For n=2, 4 and 6 cases, the realigned Hardy’s paradox can achieve Hardy values approximate 0.4140, 0.7734 and 0.8875 respectively for qubit systems, compared with only 0.09 of the original Hardy’s paradox. Meanwhile, the structure of the realigned Hardy’s paradox is simpler and more robust, in the sense that there is only one Hardy condition. We anticipate that the realigned Hardy’s paradox can tolerate more experimental imperfections and help to stimulate more fascinating quantum information applications.