Characterizing common boundaries of the quantum and the non-signaling set

Kai-Siang Chen^1*, Jun-Yi Wu², Gelo Noel M. Tabia^1,3, Chellasamy Jebarathinam^1,4, Shiladitya Mal^1,5, Yeong-Cherng Liang^1,5

¹Department of Physics, National Cheng Kung University, Tainan, Taiwan
²Department of Physics, Tamkang University, New Taipei, Taiwan
³Center for Quantum Technology, National Tsing Hua University, Hsinchu, Taiwan
⁴Center for Theoretical Physics, Polish Academy of Sciences, Warsaw, Poland
⁵Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan

* Presenter:Kai-Siang Chen, email:c24056083@gs.ncku.edu.tw

In the studies of device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. In particular, it is of paramount importance to characterize the various sets of correlations attained by locally measuring composite systems constrained by different physical principles. Among them, the principle of relativistic causality dictates that all correlations must satisfy the so-called non-signaling conditions. On the other hand, the local causality principle demands that all such correlations be Bell-local instead. Even though it is long known that the set of correlations allowed in quantum theory lies strictly between those characterized by these two principles, many questions concerning the geometry of these sets remain unanswered. Here, we report progress on this problem by fully characterizing when the boundary of the quantum set may coincide with the boundary of the non-signaling set in the simplest Bell scenario. Additionally, we give the maximally Bell-violated quantum correlation for each of the quantum achievable boundary classes and show some of them are extremal. Also, we compare the differences between quantum set and maximally entangled state set on these boundaries.

Keywords: Bell inequality, quantum correlations, non-signaling set