Device-independent entanglement quantification in the presence of losses

Shiladitya MAl^1*, Ching-Hsu Chen², Yeong-Cherng Liang³

¹Physics, National Cheng Kung University, Tainan, Taiwan
²Electronics, National Chiayi University, Chiayi, Taiwan
³Physics, National Center for Theoretical Sciences, Tainan, Taiwan

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

In pursuing new-age quantum technology, quantum entanglement has been established as a valuable resource for many tasks, such as secure communication, fast computation, and the generation of provable random bits. In a typical experimental scenario, entanglement certification is carried out assuming the dimension of the state space and the exact form of the measurements performed. These assumptions are, however, not necessarily justifiable in a realistic experimental scenario, thus making the conclusions drawn questionable. An elegant way to get around this problem is to use a Bell test and draw conclusions directly from the observed statistics showing Bell-nonlocality, i.e., to perform so-called device-independent (DI) entanglement {\em certification}. In fact, even entanglement {\em quantification} based on entanglement monotones can be carried out in a DI manner. Of course, a DI certification or quantification has to meet its own challenges. For example, since it is based on a Bell test, it is subjected to so-called locality or detection loopholes. In this work, we focus on the latter, i.e., how severe losses in a Bell test impact the task of DI entanglement quantification based on negativity, a computable measure of entanglement. Specifically, we develop a systematic approach how to characterise various sets of correlations with a fixed amount of negativity.

Keywords: Entanglement, Bell inequality, non locality, Device-independent technique, quantum information