Sequential generation of Polynomial Invariants and N-body non-local correlations

We report an inductive process that allows for a sequential construction of polynomial invariants of state coefficients for multipartite quantum states. The starting point can be a physically meaningful invariant of a smaller part of the system. The process is applied to construct a chain of invariants that quantify GHZ state like non-local N-way correlations in an N qubit pure state and the sum of N-way and (N-1)-way correlations. Analytic expressions for four and three-way correlation quantifiers for four qubits, as well as, five-way and four-way correlation quantifiers for a five qubit pure state are given.