Accessible nonlinear entanglement witnesses

TL;DR

This paper introduces accessible nonlinear entanglement witnesses that improve detection capabilities over linear witnesses, can be evaluated with existing data, and enhance entanglement verification in quantum experiments.

Contribution

The authors develop a method to construct accessible nonlinear entanglement witnesses that outperform linear ones and can be applied without additional measurements.

Findings

Nonlinear EWs detect more entangled states than linear EWs.

They can be evaluated using the same data as linear witnesses.

They enable reanalysis of existing experimental data to confirm entanglement.

Abstract

Verification of entanglement is an important tool to characterize sources and devices for use in quantum computing and communication applications. In a vast majority of experiments entanglement witnesses (EW) are used in order to prove the presence of entanglement in a quantum state. EWs can be constructed from available measurement results and do not require a reconstruction of the whole density matrix (full tomography), which is especially valuable for high-dimensional systems. We provide a method to construct {\it accessible nonlinear EWs}, which incorporate two important properties. First, they improve on linear EWs in the sense that each non-linear EW detects more entangled states than its linear counterpart and therefore allow the verification of entanglement without critical dependence on having found the 'right' linear witness. Second, they can be evaluated using exactly the same data as for the evaluation of the original linear witness. This allows a reanalysis of published experimental data to strengthen statements about entanglement verification without the requirement to perform additional measurements. These particular properties make the accessible nonlinear EWs attractive for the implementations in current experiments, for they can also enhance the statistical significance of the entanglement verification.