Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 1 ,pp. 29-35

REMARKS ON BELL'S INEQUALITY FOR SPIN CORRELATIONS

By

K. BALASUBRAMANIAN, J.C. GUPTA and K.R. PARTHASARATHY,
*Indian Statistical Institute, New Delhi*

*SUMMARY.* It is shown that Bell's inequalities (1964) for spin correlations
are sufficient for a
correlation matrix of order $\le 4$ to be the correlation matrix
of spin random variables in the classical sense. However, they
are not sufficient for matrices of order $\ge 5.$ Every
correlation matrix is realized as a quantum correlation matrix
of spin variables.

*AMS (1991) subject classification.* 62H20.

*Key words and phrases. *Bell's inequality, spin
correlations,fermion Fock space.