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摘要：The quantum entangled state, which does not violate the Bell non-locality, can violate the Bell non-locality due to the super-activation. Thus, the quantum entanglement is indeed one of the most important properties of quantum mechanics, i.e., Truth of Nature. We shall propose the quantum entanglement theory from mathematical point of view, and present its most elegant part on pure states in details, i.e., Beauty of Theory. For a general quantum system with N particles, we show that the quantum space (the total spin polarization parameter space) is complex projective space, and the classical space (the spin polarization parameter space for classical theory) is the cartesian product of the complex projective spaces. Thus, the classical space is the (generalized) Sagre variety in the quantum space, and the quantum entanglement space is the difference of these two spaces. In addition, we propose a generic method to calculate the quantum range and classical range for the expectation value of any physics observable at the collider, and can probe the quantum entanglement spaces which the previous ways cannot. However, there is a circular argument issue. Furthermore, we will briefly explain how to probe the quantum entanglement consistently in high energy physics by excluding the local hidden variable theory via angular distribution and avoiding the spin analyzing power dependence.
个人简介：李田军，河南师范大学物理学院，教授，博士生导师；曾任中国科学院理论物理研究所研究员。1991年7月于武汉大学物理系获学士学位，1994年7月于中国科学院理论物理研究所获硕士学位，2000年8月于威斯康星大学麦迪逊分校物理系获博士学位；2000年9月至2002年8月于宾西法尼亚大学物理天文系做博士后，2002年9月至2005年8月于普林斯顿高等研究院做研究人员。发表文章270余篇，引用次数8000余次，曾获得威斯康星大学麦迪逊分校 J. Van Vleck Fellowship；普林斯顿高等研究院 Fellowship；2018年享受政府特殊津贴等。