Nonlocal correlations are generic in infinite-dimensional bipartite systems

Rob Clifton, Hans Halvorson, Adrian Kent

Research output: Contribution to journalArticlepeer-review


It was recently shown that nonseparable density operators on the Hilbert space [Formula Presented] 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 [Formula Presented] where we show that states violating the Clauser-Horne-Shimony-Holt (CHSH) inequality are dense, and the case [Formula Presented] 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)
Pages (from-to)7
Number of pages1
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number4
StatePublished - 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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