学术进展
SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness
作者:
时间: 2024-09-13
阅读:
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
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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. |