NDLI: Bell Inequalities, Grothendiecks Constant, and Root Two

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Reeds, J. A. Fishburn, P. C.
Copyright Year	1994
Abstract	B. S. Tsirelson showed that comparisons between probabilities in classical physics and probabilities in quantum mechanics yield discrepancy measures $K_n $ for finite $n \times n$ real matrices that approach Grothendiecks constant $K_G $ as n gets large. It is known that $K_2 = K_3 = \sqrt{2} $ and that $K_G \geq \pi /2 = 1.57 \cdots $, but examples of $n \times n$ matrices for specified n that demonstrate $K_n > \sqrt{2} $ have eluded researchers. A series of elementary examples are provided, which yield lower bounds on $K_{k ( k - 1 )} $ that approach 3/2 as k gets large. A uniform change along the main diagonal of our basic example shows that $K_{20} \geqq = 10/7 = 1.42 \cdots $.
Starting Page	48
Ending Page	56
Page Count	9
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480191219350
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	7
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-08
Access Restriction	Subscribed
Subject Keyword	Bell inequalities correlation Combinatorial inequalities finite matrices with large discrepancies Matrices Axioms; other general questions Grothendiecks constant
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Bell Inequalities, Grothendiecks Constant, and Root Two