连续变量加权图状态局部高斯运算的图形描述
Graphical description of local Gaussian operations for continuous-variable weighted graph states
摘要：
本文提出了连续变量（CV）加权图态的局部Clifford（LC，也称为局部高斯（LG））运算的形式，它是量子比特图态的局部互补LC运算的对应形式.证明了CV加权图态的新性质，并给出了稳定器的形式化表示。它与量子比特加权图态有明显的区别，后者不能用稳定子形式表示。相应的图形规则，在纯图形理论方面，描述，这完全表征CV加权图形状态下的LC操作的演变。该LC操作可以重复地应用于CV加权图状态，其可以生成该图状态的无限LC等效图状态。这是刻画CV赋权图态的LC等价类的重要一步。
英文摘要：
The form of a local Clifford (LC, also called local Gaussian (LG)) operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit graph states. The novel property of the CV weighted graph states is shown, which can be expressed by the stabilizer formalism. It is distinctively different from the qubit weighted graph states, which can not be expressed by the stabilizer formalism. The corresponding graph rule, stated in purely graph theoretical terms, is described, which completely characterizes the evolution of CV weighted graph states under this LC operation. This LC operation may be applied repeatedly on a CV weighted graph state, which can generate the infinite LC equivalent graph states of this graph state. This work is an important step to characterize the LC equivalence class of CV weighted graph states.
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