Numerical construction of multipartite entanglement witnesses

TL;DR

This paper introduces a numerical method based on a generalized power iteration to construct multipartite entanglement witnesses, enabling detection of entanglement in complex quantum systems where exact calculations are infeasible.

Contribution

The authors develop a novel numerical approach that generalizes power iteration to solve separability eigenvalue equations for constructing optimal entanglement witnesses.

Findings

Successfully applied to complex quantum states

Demonstrates effectiveness in identifying multipartite entanglement

Provides a versatile numerical tool for quantum entanglement detection

Abstract

Entanglement in multipartite systems is a key resource for quantum information and communication protocols, making its verification in complex systems a necessity. Because an exact calculation of arbitrary entanglement probes is impossible, we derive and implement a numerical method to construct multipartite witnesses to uncover entanglement in arbitrary systems. Our technique is based on a substantial generalization of the power iteration, an essential tool for computing eigenvalues, and it is a solver for the separability eigenvalue equations, enabling the general formulation of optimal entanglement witnesses. Beyond our rigorous derivation and direct implementation of this method, we also apply our approach to several examples of complexly quantum-correlated states and benchmark its general performance. Consequently, we provide an generally applicable numerical tool for the identification of multipartite entanglement.