Axiomatic approach for the functional bound of multipartite high dimensional correlation

• We propose a formalism to derive the maximal bound of generalized Bell type correlation.
• We generate correlations whose local hidden variable bound can be obtained from the series of the constraint equations.
• Constraint equations convert the optimization problem into the counting problems whose complexity is dramatically reduced.
• Our correlation can be used to generate many other known Bell type functions.

We propose a formalism to derive the maximal bound of generalized Bell type correlation and shows that the formalism can be applied to various form of Bell functions. The Bell function is defined to generate correlations of multiparty high-dimensional system whose local hidden variable bound can be obtained from the series of the constraint equations. The application of the constraints converts the optimization problem into the counting problems whose complexity is dramatically reduced. It is also shown that the correlation can be used to generate many other known Bell type functions such as Mermin, Ardehali, Svetlichny functions for multipartite two-dimensional class.