Measurement-device-independent nonlinear entanglement witnesses

TL;DR

This work addresses measurement-device dependence in entanglement detection and extends nonlinear entanglement witnesses (NEWs) into a measurement-device-independent framework. By decomposing nonlinear functionals into input-state-assisted payoffs and incorporating maximally mixed ancillas, the authors construct measurement-device-independent nonlinear entanglement witnesses (MDI-NEWs) for both NPPT and PPT bound entangled states, showing that they certify the same entangled-state sets as their device-dependent counterparts and surpass MDI-EWs in detection power. They provide explicit constructions: for NPPT states the relation $N_\phi(P) \sim F_\phi(\rho)$ under suitable measurements, and for PPT bound entangled states a parallel construction using positive maps $M_\xi$ with a concrete 3×3 bound-entangled example; the approach remains valid for arbitrary NEWs. Overall, MDI-NEWs offer robust, device-tolerant entanglement certification with potential applicability to a broader class of nonlinear witnesses and higher-dimensional systems, enabling more reliable entanglement verification in experiments.

Abstract

Entanglement witnesses are one of the most effective methods to detect entanglement. It is known that nonlinear entanglement witnesses provide better entanglement detection than their linear counterparts, in that the former detect a strictly larger subset of entangled states than the latter. Whether linear or nonlinear, the method is measurement-device dependent, so that imperfect measurements may cause false certification of entanglement in a shared state. Measurement-device-independent entanglement witnesses provide an escape from such measurement dependence of the entanglement detection for linear entanglement witnesses. Here we present measurement-device-independent nonlinear entanglement witnesses for non-positive partial transpose entangled states as well as for bound entangled states with positive partial transpose. The constructed measurement-device-independent nonlinear entanglement witnesses certify the entanglement of the same sets of entangled states as their device-dependent parents do, and therefore are better than the linear entanglement witnesses, device-independent or otherwise.