论文标题
关于本地紧凑型组的量子断层扫描
On quantum tomography on locally compact groups
论文作者
论文摘要
我们在本地紧凑的Abelian团体$ G $上介绍量子层析成像。从$ c^*$ - 代数$ a（g）$上的量子状态集的线性地图构建了$ g $的投影统一表示形式到特征功能的空间。从$ a（g）$确定量子可观察的符号的双图被得出。给定状态的特征函数，引入了组成一组概率分布的量子断层图。我们提供了三个示例，其中$ g = {\ mathbb r} $（光学断层扫描），$ g = {\ mathbb z} _n $（对应于相互公正的基础中的测量值）和$ g = {\ mathbb t} $（相位的阶段）。作为应用程序，我们计算了量子Weyl通道的输出状态的量子断层图。
We introduce quantum tomography on locally compact Abelian groups $G$. A linear map from the set of quantum states on the $C^*$-algebra $A(G)$ generated by the projective unitary representation of $G$ to the space of characteristic functions is constructed. The dual map determining symbols of quantum observables from $A(G)$ is derived. Given a characteristic function of a state the quantum tomogram consisting a set of probability distributions is introduced. We provide three examples in which $G={\mathbb R}$ (the optical tomography), $G={\mathbb Z}_n$ (corresponding to measurements in mutually unbiased bases) and $G={\mathbb T}$ (the tomography of the phase). As an application we have calculated the quantum tomogram for the output states of quantum Weyl channels.
