For two particles with different spins, we derive the Bell's inequality. The inequality is investigated for two systems combining spin- 1 and spin- 1/2 ; spin- 1/2 and spin- 3/2. We show that for these states Bell's inequality is violated.
It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle. Here, we derive a single-particle Bell's inequality for two correlated spin states at two successive times, appealing to the statistical independence condition in an ideal experiment, for a locally causal hidden variables theory. We show that regardless of the locality assumption, the inequality can be violated by some quantum predictions.
We formulate information-theoretic Bell inequalities, which apply to any pair of widely separated physical systems. If local realism holds, the two systems must carry information consistent with the inequalities. Two spin-s particles in a state of zero total spin violate these information Bell inequalities.
The Bell inequality two-particle spin states are considered. It is shown that violation of this inequality at experimental verifications is connected with the fact that it is proved for some arbitrary random variables, but in experimental verification random variables of special type are used. A new inequality is constructed. It contains a correlation coefficient of random variables, measured at the experiment, and does not have to be violated at experimental verification. For factorizable and separable states it coincides with the usual Bell inequality.