Beijing Computational Science Research Center, Beijing 100193, China.
Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan.
Phys Rev Lett. 2018 Jun 22;120(25):250501. doi: 10.1103/PhysRevLett.120.250501.
We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the spin operators defined in the dual lattice. We investigate an extended Kitaev chain with a Z symmetry identified equivalently by winding numbers and paired Majorana zero modes at each end. The topological phases with high winding numbers are detected by the scaling coefficient of the quantum Fisher information density with respect to generators in different dual lattices. Containing richer properties and more complex structures than bipartite entanglement, the dual multipartite entanglement of the topological state has promising applications in robust quantum computation and quantum metrology, and can be generalized to identify topological order in the Kitaev honeycomb model.
我们证明了多体纠缠能够刻画一维对称保护拓扑序，这可以通过相对于双晶格中定义的自旋算符的基态量子Fisher信息的标度行为来证明。我们研究了一个具有 Z 对称的扩展 Kitaev 链，该对称可以通过缠绕数和两端的配对 Majorana 零模来等效地识别。拓扑相的高缠绕数可以通过量子Fisher信息密度相对于不同双晶格中生成元的标度系数来检测。与二体纠缠相比，拓扑态的对偶多体纠缠具有更丰富的性质和更复杂的结构，在鲁棒量子计算和量子计量学中有广阔的应用前景，并且可以推广到识别 Kitaev 蜂窝模型中的拓扑序。
