General multipartite entangled states and complex projective variety

TL;DR

This paper explores the geometric structure of multipartite quantum states and introduces a new measure of entanglement based on complex projective varieties defined by quadratic polynomials.

Contribution

It presents a novel geometric approach to quantify entanglement in multipartite states using complex projective varieties.

Findings

A geometric measure of entanglement can be constructed from complex projective varieties.

The structure of multipartite states can be characterized using quadratic polynomial-defined varieties.

Provides a new perspective on entanglement quantification in quantum information theory.

Abstract

We discuss and investigate the geometrical structure of general multipartite states. In particular, we show that a geometrical measure of entanglement for general multipartite states can be constructed by the complex projective varieties defined by quadratic polynomials.