论文标题
在局部紧凑型组上由协变正运算符值衡量标准产生的量子通道上
On quantum channels generated by covariant positive operator-valued measures on a locally compact group
论文作者
论文摘要
我们引入了正面紧凑型Abelian Group $ G $的直接产品产生的正面运营商价值措施（POVM），其双$ \ hat g $。该方法基于pontryagin二元性，允许在$ l^2（g）$中的Hilbert-Schmidt运算符和Hilbert Space $ L^2（\ Hat G \ Times G）$之间建立同构同构。任何这样的措施都决定了由测量通道和通道将初始量子状态传输到组上量子状态的集合的一对杂种（包含经典和量子零件）量子通道。结果表明，第二个通道可以称为测量通道的互补通道。
We introduce positive operator-valued measure (POVM) generated by the projective unitary representation of a direct product of locally compact Abelian group $G$ with its dual $\hat G$. The method is based upon the Pontryagin duality allowing to establish an isometrical isomorphism between the space of Hilbert-Schmidt operators in $L^2(G)$ and the Hilbert space $L^2(\hat G\times G)$. Any such a measure determines a pair of hybrid (containing classical and quantum parts) quantum channels consisting of the measurement channel and the channel transmitting an initial quantum state to the ensemble of quantum states on the group. It is shown that the second channel can be called a complementary channel to the measurement channel.
