Can the Freedom-of-Choice Loophole be Closed Merely with Genuine Randomness?
Freedom to choose the input parameters in Bell tests had not attracted much attention until T. Scheidl et al. pointed out the possible freedom-of-choice loophole that can make the Bell violation be interpreted by local realism (Proc. Natl. Acad. Sci. 107, 19708 (2010)). They claimed that this loophole could be closed by truely random setting choices, thus the deterministic local realism is excluded. In this paper, however, we raise the improved argument that random setting choices alone are not enough in closing the freedom-of-choice loophole. A deterministic local realism model based on this loophole will be proposed. In this model, we will prove that Bell violation with random setting choices is efficient in rejecting this local realism in ideal condition, but it can still exist when inefficient detectors (efficiency η ≤ 50 %) are used.
KeywordsBell violation Freedom-of-choice loophole Random setting choices Deterministic local realism model
The authors thank A. Zeilinger for his instructive comments and suggestions. Financial support from NSFC Grant Nos. 10905028, U1204616, 11204072, 61378011. Program for ScienceTechnology Innovation Talents in Universities of Henan Province (Grant No. 2012HASTIT028), Program for Science and Technology Innovation Research Team in University of Henan Province (Grant No. 13IRTSTHN020) and Science Foundation of Henan Provincial Education Department (Grant No. 2010A140010) is gratefully acknowledged. H. Lu is also supported by Hubei Provincial Department of Education under Grant No. 20121406.
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