Phys. Rev. A 73, 062105 (2006) [5 pages]Grothendieck’s constant and local models for noisy entangled quantum statesReceived 23 November 2005; published 9 June 2006 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 ρpW=p∣ψ−⟩⟨ψ−∣+(1−p)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. We generalize this result to arbitrary quantum states. © 2006 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.73.062105
DOI:
10.1103/PhysRevA.73.062105
PACS:
03.65.Ud, 03.67.Dd, 03.67.Mn
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