Large Violation of Bell Inequalities with Low Entanglement

M. Junge, C. Palazuelos

Research output: Contribution to journalArticlepeer-review


In this paper we obtain violations of general bipartite Bell inequalities of order with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.

Original languageEnglish (US)
Pages (from-to)695-746
Number of pages52
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - Sep 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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