Study of two kinds of Loopholes in Measurement Device Independent Entanglement Witness

Kornikar sen³, Chirag Srivastav³, Shiladitya Mal^1*, Aditi Sen(De)³, Ujjwal Sen³

¹Physics, NCTS, Tinan, Taiwan
²Physics, NCKU, Tainan, Taiwan
³Physics, HRI, Allahabad, India

* Presenter:Shiladitya Mal, email:shiladitya.27@gmail.com

Entanglement witnesses form an effective method to detect entanglement in the laboratory without having prior knowledge of the full density matrix. However, separable states can be erroneously indicated as entangled in the presence of wrong measurements or lossy detectors. Measurement-device-independent entanglement witnesses (MDI-EWs) never detect fake entanglement even under wrong measurements and for a particular kind of lossy detectors. We analyze here other kind of “detection loophole” in the context of MDI-EWs. We obtain an upper bound, a threshold value, on the entanglement witness function in the MDI-EW scenario, below which entanglement is guaranteed for given nonideal detector efficiencies, that can involve both lost events and dark counts. Another crucial assumption in the case of faithful detection of entanglement employing MDI-EWs is that the preparation devices producing “quantum inputs” has to be perfect. Here we relax these assumptions and derive sufficient conditions on the uniform noisy map for retaining the characteristic of MDI-EWs. We also investigate various paradigmatic models of local noise and find conditions of revealing entanglement in the class of Werner states.

Keywords: Entanglement witness, Measurement device independent, Detection loophole