Using Inequalities as Tests for the Kochen-Specker Theorem for Multiparticle States

Abstract

The Kochen-Specker theorem is investigated for n spin-1/2 systems by using an inequality proposed in Nagata (J. Math. Phys. 46, 102101, 2005) on the basis on binary logic. A measurement theory based on the truth values (binary logic), i.e., the truth T (1) for true and the falsity F (0) for false is used. The values of measurement outcome are either + 1 or 0 (in $\hbar /2$ unit). The quantum predictions by n-multipartite states violate the inequality by an amount that grows exponentially with n. The measurement theory based on the binary logic provides an exponentially stronger refutation of the existence of hidden-variable when the number of parties of the state increases more. It turns out that the Kochen-Specker theorem becomes a quite strong theorem when the dimension of the multipartite state highly increases, regardless of entanglement properties.