不可分辨粒子多体系统的纠缠
Entanglement for multipartite systems of indistinguishable particles
摘要：
我们分析了玻色子和费米子成分的多体系统的纠缠概念，并将其推广到任意的准统计系统。我们使用对称群的表示理论，根据具有适当对称性的简单张量来制定解决这个问题的统一方法。对于任意的parastatistics，我们定义的S-秩推广的施密特秩的概念。S-秩，定义为所有类型的张量，用于区分纯态的纠缠。此外，对于玻色和费米统计，我们构建了一个类似的Jamiolkowski同构。
英文摘要：
We analyze the concept of entanglement for multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics. We use the representation theory of symmetry groups to formulate a unified approach to this problem in terms of simple tensors with appropriate symmetry. For an arbitrary parastatistics, we define the S-rank generalizing the notion of the Schmidt rank. The S-rank, defined for all types of tensors, serves for distinguishing entanglement of pure states. In addition, for Bose and Fermi statistics, we construct an analog of the Jamiolkowski isomorphism.
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