Non-local Correlations are Generic in Infinite-Dimensional Bipartite Systems

Details Non-local Correlations are Generic in Infinite-Dimensional Bipartite Systems Non-local Correlations are Generic in Infinite-Dimensional Bipartite Systems

1999-09-03

arxiv.org/abs/quant-ph/9909016v2

Phys. Rev. A 61, 042101 (2000)

Physics

Quantum Physics

8 pages, RevTeX

Scientific paper

10.1103/PhysRevA.61.042101

It was recently shown that the nonseparable density operators for a bipartite system are trace norm dense if either factor space has infinite dimension. We show here that non-local states -- i.e., states whose correlations cannot be reproduced by any local hidden variable model -- are also dense. Our constructions distinguish between the cases where both factor spaces are infinite-dimensional, where we show that states violating the CHSH inequality are dense, and the case where only one factor space is infinite-dimensional, where we identify open neighborhoods of nonseparable states that do not violate the CHSH inequality but show that states with a subtler form of non-locality (often called "hidden" non-locality) remain dense.

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