David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Contemporary versions of Bell’s argument against local hidden variable (LHV) theories are based on the Clauser Horne Shimony and Holt (CHSH) inequality, and various attempts to generalize it. The amount of violation of these inequalities cannot exceed the bound set by the Grothendieck constants. However, if we go back to the original derivation by Bell, and use the perfect anticorrelation embodied in the singlet spin state, we can go beyond these bounds. In this paper we derive two-particle Bell inequalities for traceless two-outcome observables, whose violation in the singlet spin state go beyond the Grothendieck constant both for the two and three dimensional cases. Moreover, creating a higher dimensional analog of perfect correlations, and applying a recent result of Alon and his associates (Invent. Math. 163 499 (2006)) we prove that there are two-particle Bell inequalities for traceless two-outcome observables whose violation increases to in…nity as the dimension and number of measurements grow. Technically these result are possible because perfect correlations (or anti-correlations) allow us to transport the indices of the inequality from the edges of a bipartite graph to those of the complete graph. Finally, it is shown how to apply these results to mixed Werner states, provided that the noise does not exceed 20%.
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Han Geurdes (2010). CHSH and Local Causlaity. Adv Studies Theoretical Physics 4 (20):945.
Abner Shimony (1984). Contextual Hidden Variables Theories and Bell's Inequalities. British Journal for the Philosophy of Science 35 (1):25-45.
Michael Seevinck (2006). The Quantum World is Not Built Up From Correlations. Foundations of Physics 36 (10):1573-1586.
Gábor Hofer-Szabó (2011). Bell(Δ) Inequalities Derived From Separate Common Causal Explanation of Almost Perfect EPR Anticorrelations. Foundations of Physics 41 (8):1398-1413.
Rob Clifton & Damian Pope, On the Nonlocality of the Quantum Channel in the Standard Teleportation Protocol.
Thomas Filk (2011). Non-Classical Correlations in Bistable Perception? Axiomathes 21 (2):221-232.
Gábor Hofer-Szabó (2007). Separate- Versus Common -Common-Cause-Type Derivations of the Bell Inequalities. Synthese 163 (2):199 - 215.
Added to index2009-08-21
Total downloads20 ( #90,243 of 1,102,094 )
Recent downloads (6 months)1 ( #306,622 of 1,102,094 )
How can I increase my downloads?