Titre du document / Document title

Bell inequalities, Grothendieck's constant, and root two

Auteur(s) / Author(s)

FISHBURN P. C. ; REEDS J. A. ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

AT&T Bell Laboratories, Murray Hill NJ 07974, ETATS-UNIS

Résumé / 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 × n real matrices that approach Grothendieck's constant K_G as n gets large. It is known that K₂ = K₃ = √2 and that K_G ≥ π/2 = 1.57..., but examples of n × n matrices for specified n that demonstrate K_n > √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 K₂₀ ≥ 10/7 = 1.42..

Revue / Journal Title

SIAM journal on discrete mathematics   ISSN 0895-4801   CODEN SJDMEC 

Source / Source

1994, vol. 7, n^o1, pp. 48-56 (14 ref.)

Langue / Language

Anglais

Editeur / Publisher

Society for Industrial and Applied Mathematics, Philadelphia, PA, ETATS-UNIS  (1988) (Revue)

Mots-clés anglais / English Keywords

Real matrix ; Hilbert space ; Quantum theory ; Correlation matrix ;

Mots-clés français / French Keywords

Matrice réelle ; Espace Hilbert ; Théorie quantique ; Matrice corrélation ; Inégalité Bell ; Constante Grothendieck ; Racine deux ; Mesure discrépance ;

Mots-clés espagnols / Spanish Keywords

Matriz real ; Espacio Hilbert ; Teoría cuántica ; Matriz correlación ;

Localisation / Location

INIST-CNRS, Cote INIST : 21614, 35400004920931.0060