论文标题
从拓扑角度从纠缠分类
Entanglement Classification from a Topological Perspective
论文作者
论文摘要
纠缠的分类是量子资源理论中的重要问题。在本文中，我们在拓扑量子场理论（TQFT）的背景下讨论了这个问题的嵌入。这种方法允许根据拓扑等效类别对纠缠模式进行分类。在二手情况下，通过限制在简单的连接图中，通过随机局部操作和经典通信（SLOCC）等效的分类（SLOCC）。这样的图将TQFT的量子状态表征为``连接组''的编织和缠结。在多部分情况下，相同的受限拓扑分类仅捕获SLOCC类的一部分，尤其没有看到三个Qubits的W纠缠。连接的非本地编织可能会解决该问题，但是在这种情况下，没有尝试过有限的分类。尽管不完整，但Connectome分类对当事方的任何数字和维度都有直接的概括，并且具有非常直观的解释，这对于理解纠缠的特定属性和设计新量子资源可能很有用。
Classification of entanglement is an important problem in Quantum Resource Theory. In this paper we discuss an embedding of this problem in the context of Topological Quantum Field Theories (TQFT). This approach allows classifying entanglement patterns in terms of topological equivalence classes. In the bipartite case a classification equivalent to the one by Stochastic Local Operations and Classical Communication (SLOCC) is constructed by restricting to a simple class of connectivity diagrams. Such diagrams characterize quantum states of TQFT up to braiding and tangling of the ``connectome.'' In the multipartite case the same restricted topological classification only captures a part of the SLOCC classes, in particular, it does not see the W entanglement of three qubits. Nonlocal braiding of connections may solve the problem, but no finite classification is attempted in this case. Despite incompleteness, the connectome classification has a straightforward generalization to any number and dimension of parties and has a very intuitive interpretation, which might be useful for understanding specific properties of entanglement and for design of new quantum resources.
