Many-body entanglement measure

course paper for Mathematical Physics Methods, 2021-06-27


For a quantum system, there's usually complex entanglement among its subsystems, and entropy can evaluate it. Von Neuuman entropy can accurately estimate a subsystem's entanglement with the rest of the system in a pure state, but so far there hasm't been a standard procedure to measure multipartite entanglement in a mixed state. In this paper, we introduce the basic concepts of quantum entanglement and entropy, including Von Neuuman entropy and its basic properties, and the method to measure entanglement in a pure state with Von Neuuman entropy. We also introduce concurrence and 3-tangle to measure bipartite and tripartite entanglement, and its problem when generalized to an N-body case. We compare the state-of-the-art 6 measurements of entropy including distillable entropy and entropy of formation, and evaluate their basic properties and rationality as an entropy.

对于一个量子系统而言,其子体系间往往存在复杂的纠缠,而熵可以衡量系统的子体系和整个系统的纠缠。冯诺依曼熵可以精确地衡量纯态下子体系与外界的的纠缠状态,而混态下的多体纠缠至今目前为止没有标准的衡量手段。本文介绍了量子纠缠和熵的基本概念,包括香农熵和冯·诺依曼熵及其基本性质,以及用冯诺依曼熵衡量纯态下纠缠的方法。本文还分别介绍了concurrence和3-tangle对于两体和三体纠缠的衡量方法,以及在多体问题中推广的合理性和问题。除此之外,我们比较了文献中所提出的包括蒸馏熵、生成纠缠等在内的对于混态下纠缠的6 种衡量方法,考察了其作为熵的基本性质及其合理性。


Tian-Shen He 何天深
Jun-Han Huang 黄俊涵
Yu-Feng Zhu 朱宇峰
Yi-Zi Feng 冯译子
Ze Li 李泽


The paper is available at here.