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

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.

Notation improved and typos corrected

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Cited by in corpus (3)

• Upper bound on three tangles of reduced states of four-qubit pure states
• On Monogamy of four qubit entanglement
• Monogamy constraints on entanglement of four-qubit pure states