dorsal/arxiv
View SchemaGrothendieck's constant and local models for noisy entangled quantum states
| Authors | Antonio Acin, Nicolas Gisin, Benjamin Toner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606138 |
| URL | https://arxiv.org/abs/quant-ph/0606138 |
| DOI | 10.1103/PhysRevA.73.062105 |
| Journal | Phys. Rev. A 73, 062105 (2006) |
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 $\rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}$, we show that there is a local model for projective measurements if and only if $p \le 1/K_G(3)$, where $K_G(3)$ is Grothendieck's constant of order 3. Known bounds on $K_G(3)$ prove the existence of this model at least for $p \lesssim 0.66$, quite close to the current region of Bell violation, $p \sim 0.71$. We generalize this result to arbitrary quantum states.
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"abstract": "We relate the nonlocal properties of noisy entangled states to Grothendieck\u0027s\nconstant, a mathematical constant appearing in Banach space theory. For\ntwo-qubit Werner states $\\rho^W_p=p \\proj{\\psi^-}+(1-p){\\one}/{4}$, we show\nthat there is a local model for projective measurements if and only if $p \\le\n1/K_G(3)$, where $K_G(3)$ is Grothendieck\u0027s constant of order 3. Known bounds\non $K_G(3)$ prove the existence of this model at least for $p \\lesssim 0.66$,\nquite close to the current region of Bell violation, $p \\sim 0.71$. We\ngeneralize this result to arbitrary quantum states.",
"arxiv_id": "quant-ph/0606138",
"authors": [
"Antonio Acin",
"Nicolas Gisin",
"Benjamin Toner"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.062105",
"journal_ref": "Phys. Rev. A 73, 062105 (2006)",
"title": "Grothendieck\u0027s constant and local models for noisy entangled quantum states",
"url": "https://arxiv.org/abs/quant-ph/0606138"
},
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