The statistical strength of nonlocality proofs

W. Dam, van, R.D. Gill, P.D. Grünwald

Research output: Contribution to journalArticleAcademicpeer-review

45 Citations (Scopus)


There exist numerous proofs of Bell's theorem, stating that quantum mechanics is incompatible with local realistic theories of nature. Here the strength of such nonlocality proofs is defined in terms of the amount of evidence against local realism provided by the corresponding experiments. Statistical considerations show that the amount of evidence should be measured by the Kullback-Leibler (KL) or relative entropy divergence. The statistical strength of the following proofs is determined: Bell's original proof and Peres' optimized variant of it, and proofs by Clauser, Horne, Shimony, and Holt (CHSH), Hardy, Mermin, and Greenberger, Horne, and Zeilinger (GHZ). The GHZ proof is at least four and a half times stronger than all other proofs, while of the two-party proofs, the one of CHSH is the strongest.
Original languageEnglish
Pages (from-to)2812-2835
JournalIEEE Transactions on Information Theory
Issue number8
Publication statusPublished - 2005


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