Device-independent certification of desirable properties with a confidence interval

Kai-Giun Chen^1*, Pei-Sheng Lin¹, Yeong-Cherng Liang¹

¹Department of Physics, National Cheng Kung University, Tainan, Taiwan

* Presenter:Kai-Giun Chen, email:iverson0987509967@gmail.com

In the development of quantum technologies, a reliable means for characterizing devices, be it a measurement device or a state-preparation device, is of crucial importance. Conventional approach based on, for example, quantum state tomography or process tomography, however, relies on assumptions that are often not justifiable in a realistic experimental setting. While the device-independent approach to this problem does get around the aforementioned shortcomings by making only minimal, justifiable assumptions, most of the theoretical proposals given to date only work in the very idealized setting where independent and identically distributed (i.i.d.) trials are assumed. Here, by generalizing the analysis given in Liang and Zhang [Entropy {\bf 21}, 185 (2019)], we describe how the prediction-based-ratio method developed for hypothesis testing can be applied in the present context to achieve a device-independent certification of desirable properties with confidence interval. We provide explicit examples illustrating the efficacy of this method based on the certification of a lower bound on the negativity of the underlying state.

Keywords: quantum nonlocality, Bell test, device-independent, hypothesis testing