Bridging the Theory and Experiment for Device-Independent Quantum Information
Pei-Sheng Lin1*, Denis Rosset1, Yanbao Zhang2,3, Yeong-Cherng Liang1
1Department of Physics, National Cheng Kung University, Tainan, Taiwan
2Institute for Quantum Computing, University of Waterloo, Waterloo, Canada
3Department of Physics and Astronomy, University of Waterloo, Waterloo, Canada
* presenting author:Pei-Sheng Lin,
Device-independent quantum information is a rapidly emerging research area that exploits fundamental ideas developed in the study of quantum nonlocality. The key merit of this paradigm is that conclusions can be drawn directly from the observed correlation between measurement outcomes without relying on any assumption about the dimension of the underlying quantum state, nor the measurements implemented in the respective devices. While being a robust technique for quantum state and measurement characterization, there currently remains an important gap between the theoretical tools developed for such purposes and the experimentally obtained raw data. On the one hand, due to finite sample size, the raw correlation observed generically does not satisfy the so-called non-signaling condition. Whereas on the other hand, theoretical tools developed for device-independent analysis either explicitly or implicitly assume the non-signaling condition (which is satisfied by quantum correlation). In this work, we report a systematic study on some algorithmic procedures that may allow one to bridge this gap (under the independent and identically distributed, i.e., i.i.d. assumption). For each of these procedures, we analyze the nature of the output non-signaling distribution(s), such as their uniqueness, their biasedness with respect to certain natural figures of merit, their rate of convergence to the ideal quantum distribution as well their chance of passing the quantum membership test as a function of the sample size. Under the assumption that these procedures serve as legitimate tools for bridging the gap between the theoretical tools developed for device-independent analysis and experimentally observed raw data, we also gain insight on the minimal sample size needed for running a device-independent experiment.

Keywords: Device-independent quantum information, finite statistics, quantum correlations, Bell inequalities , non-local correlations