学术进展

SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness

论文作者:

Wen-Na Zhao, Youwang Xiao, Ming Li, Li Xu, Shao-Ming Fei

论文题目:

SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness

发表期刊:

Physica Scripta      
99 (2024) 105114

简介:

Bell non-locality is closely related with device independent quantum randomness. In this paper, we
present a kind of sum-of-squares (SOS) decomposition for general Bell inequalities in two qubits
systems. By using the obtained SOS decomposition, we can then find the measurement operators
associated with the maximal violation of considered Bell inequality.Wealso practice the SOS
decomposition method by considering the (generalized) Clauser-Horne-Shimony-Holt (CHSH) Bell
inequality, the Elegant Bell inequality, the Gisin inequality and the Chained Bell inequality as
examples. The corresponding SOS decompositions and the measurement operators that cause the
maximum violation values of these Bell inequalities are derived, which are consistent with previous
results.Wefurther discuss the device independent quantum randomness by using the SOS
decompositions of Bell inequalities.Wetake the generalized CHSHinequality with the maximally
entangled state and the Werner state that attaining the maximal violations as examples. Exact value or
lower bound on the maximal guessing probability using the SOS decomposition are obtained. For
Werner state, the lower bound can supply a much precise estimation of quantum randomness when p
tends to 1.第12题_看新晴@微信_20240910_微信图片_20240910162739_1.png