# Grothendieck's constant and local models for noisy entangled quantum states

@article{Acn2006GrothendiecksCA,
title={Grothendieck's constant and local models for noisy entangled quantum states},
author={Antonio Ac{\'i}n and Nicolas Gisin and Ben Toner},
journal={Physical Review A},
year={2006},
volume={73},
pages={062105}
}
• Published 9 June 2006
• Mathematics
• Physical Review A
We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states rho p W =p|psi–><psi–|+(1–p)[openface 1]/4, we show that there is a local model for projective measurements if and only if p<=1/KG(3), where KG(3) is Grothendieck's constant of order 3. Known bounds on KG(3) prove the existence of this model at least for p<~0.66, quite close to the current region of Bell violation, p~0.71…

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