Comparing Recent Approaches of Device-Independent Bounds on Entanglement, Steerability, and Measurement Incompatibility
Shin-Liang Chen1*, Costantino Budroni2, Yeong-Cherng Liang1, Yueh-Nan Chen1
1Department of Physics, National Cheng Kung Univerisity, Taiwan
2Institute for Quantum Optics and Quantum Information (IQOQI), Austria
* Presenter:Shin-Liang Chen,
In recent work [Phys. Rev. Lett. 116, 240401 (2016)] we proposed a framework for quantifying steerability and measurement incompatibility in a device-independent (DI) scenario. More precisely, a lower bound on steerability, measured by the steering robustness or the steerable weight, is obtained when given a nonlocal correlation. We further proved the steering robustness is a lower bound of incompatibility robustness (a measure of incompatible measurements), therefore our approach automatically provided a lower bound on the degree of measurement incompatibility when performing a Bell-type experiment. Finally, since the steering robustness has been shown to be a lower bound on the entanglement robustness, our bounds also provided an estimation of entanglement in a DI manner.

At the meantime, the other work [Phys. Rev. A 93, 052112 (2016)] by Cavalcanti and Skrzypczyk also quantified steerability and measurement incompatibility in a DI scheme. Different from our approach, they directly investigated the quantitative relations between the incompatibility robustness, the steering robustness, and the nonlocal robustness. As results, they proved that the nonlocal robustness is a lower bound on the entanglement robustness, and the consistent nonlocal robustness (another measure of nonlocality by constraining the noisy correlation) is a lower bound on the incompatibility robustness.

Motivated by the above two works, the aims of this work are: (1) Comparing DI bounds on some measures of steerability (2) Comparing DI bounds on the incompatibility robustness, and (3) comparing DI bounds on the entanglement robustness.

Keywords: quantum nonlocality, quantum entanglement, quantum steering, device-independent quantum information, measurement incompatibility