Nonlocal correlations are generic in infinite-dimensional bipartite systems

Rob Clifton, Hans Halvorson, Adrian Kent

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


It was recently shown that nonseparable density operators on the Hilbert space H1⊗H2 are trace norm dense if either factor space has infinite dimension. We show here that nonlocal states, i.e., states whose correlations cannot be reproduced by any local hidden variable model, are also dense. Our constructions distinguish between the case dim H1 = dim H2 = ∞, where we show that states violating the Clauser-Horne-Shimony-Holt (CHSH) inequality are dense, and the case dim H1<dimH2=∞, where we identify open neighborhoods of nonseparable states that do not violate the CHSH inequality but show that states with a subtler form of nonlocality (often called "hidden" nonlocality) remain dense.

Original languageEnglish (US)
Article number042101
Pages (from-to)421011-421017
Number of pages7
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number4
StatePublished - Apr 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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