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English

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

Publication date2006
Abstract

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 ρWp=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.

Citation (ISO format)
ACIN, Antonio, GISIN, Nicolas, TONER, Benjamin. Grothendieck’s constant and local models for noisy entangled quantum states. In: Physical review, A, Atomic, molecular, and optical physics, 2006, vol. 73, n° 6, p. 062105. doi: 10.1103/PhysRevA.73.062105
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ISSN of the journal1050-2947
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