Basics of perfect communication through quantum networks
Basics of perfect communication through quantum networks
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DOI：
10.1103/physreva.84.022337
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发表时间：
2011-08-25
影响因子：
2.9
通讯作者：
Kay, Alastair
中科院分区：
文献类型：
--
作者：
Kay, Alastair
量子态通过一维链的完美转移现在已经被很好地理解了，这不仅允许人们决定一个固定的哈密顿量是否实现了完美转移，而且允许人们设计一个合适的哈密顿量。我们特别感兴趣的是能够设计或理解哈密顿受到各种自然产生的约束的限制，例如具有低连接性的有限耦合拓扑(由图指定)和相互作用的类型。在这篇文章中，我们刻画了通过网络传输的充要条件，并描述了一些自然结果，如对于一大类哈密顿量，许多不同接收者之间不可能进行路由，以及对传输速率的限制。作为导出条件的结果，我们还考虑了均匀耦合网络(海森堡模型和XX模型)中传输距离和网络大小之间的一些权衡。
Perfect transfer of a quantum state through a one-dimensional chain is now well understood, allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer but to design a suitable one. We are particularly interested in being able to design, or understand the limitations imposed upon, Hamiltonians subject to various naturally arising constraints such as a limited coupling topology with low connectivity (specified by a graph) and type of interaction. In this paper, we characterize the necessary and sufficient conditions for transfer through a network and describe some natural consequences such as the impossibility of routing between many different recipients for a large class of Hamiltonians and the limitations on transfer rate. We also consider some of the trade-offs that arise in uniformly coupled networks (both Heisenberg and XX models) between transfer distance and the size of the network as a consequence of the derived conditions.