Iterations of nonlinear entanglement witnesses

TL;DR

This paper introduces an iterative method to enhance linear entanglement witnesses with nonlinear terms, resulting in stronger detection capabilities that can eventually identify all detectable entangled states.

Contribution

It presents a novel iterative approach to improve entanglement witnesses using quadratic nonlinear terms, optimizing detection for specific states.

Findings

Iterative nonlinear witnesses outperform linear ones in detecting entanglement.

The method converges to detect all states identified by the original positive map.

Optimization of the iteration enhances detection strength for targeted states.

Abstract

We describe a generic way to improve a given linear entanglement witness by a quadratic, nonlinear term. This method can be iterated, leading to a whole sequence of nonlinear witnesses, which become stronger in each step of the iteration. We show how to optimize this iteration with respect to a given state, and prove that in the limit of the iteration the nonlinear witness detects all states that can be detected by the positive map corresponding to the original linear witness.