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Here, we consider the Bell experiment for a system described by multipartite states in the case where n-dichotomic observables are measured per site. If n is two, we consider a two-setting Bell experiment. If n is three, we consider a three-setting Bell experiment. Two-setting model is an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment. Three-setting model is an explicit local realistic model for the values of a correlation function, given in a three-setting Bell experiment. In the non-contextual scenario, there is not the difference between three-setting model and two-setting model. And we cannot classify local realistic theories in this case. This says that we can construct three-setting model from two-setting model. Surprisingly we can discuss incompleteness in the Bell theorem using non-contextual model. On the other hand, in the contextual scenario, there is the difference between three-setting model and two-setting model. This says that we must distinguish three-setting model from two-setting model. And we can classify local realistic theories in this case. [ABSTRACT FROM AUTHOR]

Two quantum algorithms of finding the roots of a polynomial function f(x) = xm + am− 1xm− 1 +... + a1x + a0 are discussed by using the Bernstein-Vazirani algorithm. One algorithm is presented in the modulo 2. The other algorithm is presented in the modulo d. Here all the roots are in the integers Z. The speed of solving the problem is shown to outperform the best classical case by a factor of m in both cases. [ABSTRACT FROM AUTHOR]

We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values {a1,a2,a3,…,aN} and a function g:R→{0,1}, we shall determine the following values {g(a1),g(a2),g(a3),…,g(aN)} simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Next, we consider it as a number in binary representation; M1 = (g(a1),g(a2),g(a3),…,g(aN)). By using M parallel quantum systems, we have M numbers in binary representation, simultaneously. The speed of obtaining the M numbers is shown to outperform the classical case by a factor of M. Finally, we calculate the product; M1×M2×⋯×MM. The speed of obtaining the product is shown to outperform the classical case by a factor of N × M. [ABSTRACT FROM AUTHOR]