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 http://resolver.caltech.edu/CaltechAUTHORS:ACIpra06
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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<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.
| Item Type: | Article |
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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 |
| Record Number: | CaltechAUTHORS:ACIpra06 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:ACIpra06 |
| Alternative URL: | http://dx.doi.org/10.1103/PhysRevA.73.062105 |
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 3591 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Archive Administrator |
| Deposited On: | 18 Jun 2006 |
| Last Modified: | 26 Dec 2012 08:55 |
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