论文标题
用量子组对称性的量子通道
Quantum channels with quantum group symmetry
论文作者
论文摘要
在本文中，我们将证明任何紧凑型量子组都可以用作量子通道的对称组，这使我们达到了协变量通道的概念。然后，我们通过在相关的融合规则的假设下识别所有极端条件下的所有极端点来发掘协变量通道的凸的结构，这对一些最近的结果提供了广泛的概括。量子组对称性与组对称性的对称的存在将在量子排列组和$ su_q（2）$的示例中突出显示。在后一个示例中，我们将看到Heisenberg图片来自非KAC类型条件的必要性。本文以相互协方差在投射表示方面结束，这使我们回到了Weyl协方差渠道及其费米子类似物。
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant channels by identifying all extreme points under the assumption of multiplicity-free condition for the associated fusion rule, which provides a wide generalization of some recent results. The presence of quantum group symmetry contrast to the group symmetry will be highlighted in the examples of quantum permutation groups and $SU_q(2)$. In the latter example, we will see the necessity of the Heisenberg picture coming from the non-Kac type condition. This paper ends with the covariance with respect to projective representations, which leads us back to Weyl covariant channels and its fermionic analogue.
