We report an inductive process that allows for sequential construction of local unitary invariant polynomials 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 non-local N-way correlations in an N-qubit pure state. It also yields the invariants to quantify the sum of N-way and (N-1)-way correlations. Analytic expressions for four-way and three-way correlation quantifiers for four-qubit states, as well as, five-way and four-way correlation quantifiers for five-qubit pure states are given.
['S. Shelly Sharma', 'N. K. Sharma']
Sequential generation of Polynomial Invariants and N-body non-local correlations