A New Loophole in Recent Bell Test Experiments

Abstract

Recent experiments have reached detection efficiencies sufficient to close the detection loophole with photons. Both experiments ran multiple successive trials in fixed measurement configurations, rather than randomly re-setting the measurement configurations before each measurement trial. This opens a new potential loophole for a local hidden variable theory. The loophole invalidates one proposed method of statistical analysis of the experimental results, as demonstrated in this note. Therefore a different analysis will be necessary to definitively assert that these experiments are subject only to the locality loophole. a a Comment, May 2015: The last sentence of the abstract and the last two paragraphs of this work call for a new form of statistical analysis. A recent work, "Bell inequalities for continuously emitting sources" (E. Knill et al., Phys. Rev. A (2015) 91, 032105), has provided such an analysis, and this analysis has been applied to experimental data sets in arXiv:1503.07573 (B.G. Christensen et al.).

A robust mathematical model for a loophole-free Clauser–Horne experiment

“…While it may theoretically be possible to implement a loophole-free test of a Bell inequality with such a "block-measurement" experimental design, this scenario poses additional challenges for statistical analysis. These challenges are more fully explored in [23], but we touch on the main points here.…”

“…Furthermore, even if this degree of separation could be achieved, it is an open question whether there is a statistical analysis that could distinguish between quantum mechanics and local theories in a block-measurement design. A proposed solution in the online supporting material of [2] has flaws, as detailed in [23], but an upcoming work may soon resolve this question [24].…”

“…because P (Y k = s j ∩ X k i ) = 0 unless j = l, and the event {Y k = s j } contains the event X j i . Now, if we re-write (23) as…”

“…Even if such large degrees of separation could be achieved, it is a difficult theoretical task to derive a statistical analysis that could distinguish between quantum mechanics and local theories in a block-measurement design. A proposed method in the online supporting material of [2] has flaws, as detailed in [21]. A more recent work [22] introduces a suitable method for such a statistical analysis.…”