Polynomial method to study the entanglement of pure N-qubit states

TL;DR

This paper introduces a polynomial-based mapping for pure N-qubit states that fully characterizes their entanglement properties, enabling the determination of separability and unentangled qubits.

Contribution

It presents a novel polynomial method that uniquely encodes pure N-qubit states and allows for analysis of their entanglement structure.

Findings

Polynomial roots characterize the state completely

Method determines separability of N-qubit states

Identifies the number of unentangled qubits

Abstract

We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the number of unentangled qubits of pure N-qubit states.