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

TL;DR

This paper introduces an inductive method to construct polynomial invariants for multipartite quantum states, enabling quantification of complex non-local correlations like GHZ states in multi-qubit systems.

Contribution

It presents a novel inductive process for sequentially building polynomial invariants from smaller subsystems, providing explicit formulas for multi-qubit correlation quantifiers.

Findings

Constructed invariants quantify N-way and (N-1)-way correlations.

Derived explicit formulas for four and five-qubit correlation measures.

Demonstrated the method's applicability to multipartite quantum states.

Abstract

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.