# Beating detection loophole in nonlinear entanglement witnesses

## TL;DR

This paper demonstrates methods to reliably detect entanglement in quantum states despite imperfect detectors, by developing nonlinear entanglement witnesses that close the detection loophole for various entangled states.

## Contribution

It introduces nonlinear entanglement witnesses capable of overcoming detection inefficiencies for both NPT and PPT entangled states.

## Key findings

- Nonlinear witnesses can reliably detect entanglement despite finite detector efficiencies.
- The approach closes the detection loophole for bound entangled states with positive partial transpose.
- Methods are applicable to a broad class of entangled states with practical detector limitations.

## Abstract

Detectors in the laboratory are often unlike their ideal theoretical cousins. They have non-ideal efficiencies, which may then lead to non-trivial implications. We show how it is possible to predict correct answers about whether a shared quantum state is entangled in spite of finite detector efficiencies, when the tool for entanglement detection is a nonlinear entanglement witness. We first consider the detection loophole for shared quantum states with nonpositive partial transpose. We subsequently find nonlinear witness operators for bound entangled states with positive partial transpose, and show how the detection loophole can be closed also in such instances.