Bell Nequality And The Ull Uantum Heory Iolated By It

Bell inequalities(BIs)derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization.The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration,while,the inequality formulated by Clauser-Horne-Shimony-Holt remains not changed.The violation of BIs indeed resulted from the quantum non-local correlation for spin-1/2 case.However,the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two spins.The spin parity effect originally demonstrated with the antiparallel spin-polarizations(Mod.Phys.Lett.B28,145004)still exists for the parallel case.The quantum non-locality does not lead to the violation for integer spins due to the cancellation of non-local interference effects by the quantum statistical-average.Again the violation of BIs seems a result of the measurement induced nontrivial Berry-phase for half-integer spins.The two Bell inequalities corresponding to spin-parallel and anti-parallel states can be written as a unified inequality.The basic properties of the unity inequality are the same as those of the original inequality.,and the maximum violation of value of the unity inequality not change,is 2,the corresponding state is the largest entangled state.The unified inequality is also not violated when the spin is 1.However,the probability value of the components in the mixed state and the coefficients of the state will directly affect the correlation average value.When two types of entanglement states,spin-polarized parallel and anti-parallel,are mixed,if the probabilities of the two states are each 1/2,the correlation average is zero under the coefficients of the specific state.The mixed state affects the correlation of particles.