Fair-sampling assumption is not necessary for testing local realism

Dominic W. Berry, Hyunseok Jeong, Magdalena Stobińska, Timothy C. Ralph

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


Almost all Bell inequality experiments to date have used postselection and therefore relied on the fair sampling assumption for their interpretation. The standard form of the fair sampling assumption is that the loss is independent of the measurement settings, so the ensemble of detected systems provides a fair statistical sample of the total ensemble. This is often assumed to be needed to interpret Bell inequality experiments as ruling out hidden-variable theories. Here we show that it is not necessary; the loss can depend on measurement settings, provided the detection efficiency factorizes as a function of the measurement settings and any hidden variable. This condition implies that Tsirelson's bound must be satisfied for entangled states. On the other hand, we show that it is possible for Tsirelson's bound to be violated while the Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality still holds for unentangled states, and present an experimentally feasible example.

Original languageEnglish
Article number012109
Pages (from-to)1-11
Number of pages11
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number1
Publication statusPublished - 13 Jan 2010

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