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

Acín, Antonio and Gisin, Nicolas and Toner, Benjamin (2006) Grothendieck's constant and local models for noisy entangled quantum states. Physical Review A, 73 (6). Art. No. 062105. ISSN 1050-2947. doi:10.1103/PhysRevA.73.062105.

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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<sub>p</sub><sup>W</sup>=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. We generalize this result to arbitrary quantum states.

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Additional Information:©2006 The American Physical Society (Received 23 November 2005; published 9 June 2006) This work is supported by the National Science Foundation under Grant No. EIA-0086038, a Spanish MCyT “Ramón y Cajal” grant, the Generalitat de Catalunya, the Swiss NCCR “Quantum Photonics,” and OFES within the European project RESQ [Grant No. IST-2001-37559]. We thank Steven Finch for providing us with Ref. [26].
Subject Keywords:quantum entanglement; quantum noise; Banach spaces
Issue or Number:6
Record Number:CaltechAUTHORS:ACIpra06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3591
Deposited By: Archive Administrator
Deposited On:18 Jun 2006
Last Modified:08 Nov 2021 19:57

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