基于CHSH不等式几何解释的“X”态量子非局域关联检验

Quantum nonlocal test of“X”state based on geometric interpretation of CHSH inequality

量子非局域关联现象是量子理论区别于经典理论的重要特征之一.“X”态作为一种典型的量子混合态,基于其进行的量子非局域关联的检验研究,不论对验证量子理论的正确性,还是在量子信息论的应用领域研究,都具有重要的意义.本文在基于传统Clauser-Horne-Shimony-Holt(CHSH)不等式进行量子非局域关联检验的基础上,提出了一种基于“X”态几何解释的量子非局域关联检验策略.利用“X”态的几何解释策略,可使物理图像更为直观地研究检验时最优化测量基选取,以及可获得的最大CHSH不等式检验值等.最后给出了基于CHSH不等式几何解释策略,“X”态成功进行量子非局域关联检验的参数范围.

Quantum nonlocal correlation is one of the important features that distinguish the quantum theory from classical theory.As a typical quantum mixed state,the study of quantum nonlocal correlation based on the"X"state is of great importance for the verification of the correctness of quantum theory and the application of quantum information theory.In this work,with the traditional Clauser-Horne-Shimony-Holt(CHSH)inequality testing for quantum nonlocal correlations,we propose a strategy for testing the quantum nonlocal correlations based on the geometric interpretation of the"X"state.By using the geometric interpretation of the"X"state,which is described by the transform of Bloch sphere,it is possible to investigate the optimal selection of measurement settings.The maximum value of CHSH inequalities can also obtained from the physical images.Finally,the range of parameters for a successful quantum nonlocal correlation testing based on the CHSH inequality for the"X"state is studied.The results show that when f=1,the"X"state will be reduced to a normal pure entangled state,and the quantum nonlocal correlation testing results are in full agreement with the traditional ones.This result proves the correctness of the geometric interpretation strategy proposed in this work.When f<1,only some of the"X"states can be used for e successfully testing the quantum nonlocal correlations.It is also found that the range of fidelity values that can successfully test the quantum nonlocal correlations will be further increased by increasing the values of r.In particular,when r=1,the range of fidelity value will reach a largest one(e.g.f>0.781).The results in this work can provide the reference for experimentally testing the quantum nonlocal correlation by using the"X"state.