Non-local games and optimal steering at the boundary of the quantum set

Yi-Zheng Zhen, Koon Tong Goh, Yu-Lin Zheng, Wen-Fei Cao, Xingyao Wu, Kai Chen, Valerio Scarani

Published 2016-02-19Version 1

The boundary between classical and quantum correlations is well characterised by linear constraints called Bell inequalities. It is much harder to characterise the boundary of the quantum set itself in the space of no-signaling correlations. By looking at the question from the perspective of non-local games based on steering, Oppenheim and Wehner [Science 330, 1072 (2010)] found an intriguing property of specific points of the quantum boundary: the local state of Bob is steered to one that saturates a local fine-grained uncertainty relation. In this paper, we extend this observation to a much larger set of points, and show that recently reported counterexamples can be circumvented by exploiting the arbitrariness in the definition of a game. These results hint to the possibility that the Oppenheim-Wehner observation holds for the whole of the quantum boundary.