Local quantum measurement and no-signaling imply quantum correlations.

@article{Barnum2010LocalQM,
  title={Local quantum measurement and no-signaling imply quantum correlations.},
  author={Howard Barnum and Salman Beigi and Sergio Boixo and Matthew B. Elliott and Stephanie Wehner},
  journal={Physical review letters},
  year={2010},
  volume={104 14},
  pages={
          140401
        }
}
We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product… 
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