No Laplacian Perfect State Transfer in Trees
No Laplacian Perfect State Transfer in Trees
复制标题
DOI：
10.1137/140989510
复制
发表时间：
2014-08
期刊：
影响因子：
--
通讯作者：
G. Coutinho;Henry Liu
中科院分区：
文献类型：
--
作者：
G. Coutinho;Henry Liu
我们考虑一个由海森堡哈密顿量控制的最近邻相互作用耦合的量子比特系统。我们进一步假设所有耦合常数都等于1。我们感兴趣的是确定哪些图允许保真度等于1的量子态转移。要回答这个问题，考虑图的拉普拉斯矩阵在适当维数的向量空间中的作用就足够了。我们的主要结果是，如果底层图是一棵树，有两个以上的顶点，那么完美的状态转移不会发生。我们还探讨了相关的问题，如发生在二分图和图与奇数的生成树。最后，我们考虑了基于$XY$-Hamilton的模型，其作用等价于图的邻接矩阵的作用。在这种情况下，我们推测，完美的状态转移不会发生在树与三个以上的顶点。
We consider a system of qubits coupled via nearest-neighbor interaction governed by the Heisenberg Hamiltonian. We further suppose that all coupling constants are equal to 1. We are interested in determining which graphs allow for a transfer of quantum state with fidelity equal to 1. To answer this question, it is enough to consider the action of the Laplacian matrix of the graph in a vector space of suitable dimension. Our main result is that if the underlying graph is a tree with more than two vertices, then perfect state transfer does not happen. We also explore related questions, such as what happens in bipartite graphs and graphs with an odd number of spanning trees. Finally, we consider the model based on the $XY$-Hamiltonian, whose action is equivalent to the action of the adjacency matrix of the graph. In this case, we conjecture that perfect state transfer does not happen in trees with more than three vertices.