Symmetries in Bell-inequality violation

Hsin-Yu Hsu^1,2*, Gelo Noel M. Tabia^1,2,3, Kai-Siang Chen^1,2, Bo-An Tsai^1,2, Yeong-Cherng Liang^1,2,3

¹Department of Physics, Center for Quantum Frontiers of Research & Technology (QFort), Tainan, Taiwan
²Department of Physics, National Cheng Kung University, Tainan, Taiwan
³Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan

* Presenter:Hsin-Yu Hsu, email:L26101125@gs.ncku.edu.tw

Symmetry plays an important role in physics. To this end, one may wonder when the maximal quantum violation of a Bell inequality is necessarily achieved by a symmetrical strategy. In general, for a Bell inequality lacking such a symmetry, there may be a gap between the maximal Bell inequality violation achievable with and without assuming such a symmetry for the underlying strategy. Even for a Bell inequality that has a certain symmetry, there is no guarantee that its maximal quantum violation can be achieved by employing a symmetrical strategy that is also minimal in dimension. Here, we consider some simple Bell inequalities and find that their maximal quantum violation is indeed attainable using a symmetrical strategy with minimal Hilbert space dimension.

Keywords: Quantum nonlocality, Quantum correlction, Symmetry