论文标题
纹状体正图和量子信息中应用的分解
Decomposition of tracial positive maps and applications in quantum information
论文作者
论文摘要
$ c^*$ - 代数之间的每个积极的多线图分别弱$^*$ - 连续。我们表明，联合弱$^*$ - 连续性等于$ c^*$ - 代数的乘法的联合弱$^*$ - 正在考虑的代数。 We study the behavior of general tracial positive maps on properly infinite von Neumann algebras and by applying the Aron--Berner extension of multilinear maps, we establish that under some mild conditions every tracial positive multilinear map between general $C^*$-algebras enjoys a decomposition $Φ=φ_2 \circ φ_1$, in which $φ_1$ is a tracial positive linear map with the交换范围和$φ_2$是带有交换域的奇特完全正面地图。直接的结果，曲折的正多线性图是完全正面的。此外，我们证明，如果$ c^*$ - 代数是von neumann代数之间的一般奇特完全正面地图$φ$的域，则$φ$具有类似的分解。作为应用程序，我们通过任意正图研究了量子力学中的广义方差和协方差。除其他外，还提出了在复合物理系统中可观察到的不平等性不平等。
Every positive multilinear map between $C^*$-algebras is separately weak$^*$-continuous. We show that the joint weak$^*$-continuity is equivalent to the joint weak$^*$-continuity of the multiplications of $C^*$-algebras under consideration. We study the behavior of general tracial positive maps on properly infinite von Neumann algebras and by applying the Aron--Berner extension of multilinear maps, we establish that under some mild conditions every tracial positive multilinear map between general $C^*$-algebras enjoys a decomposition $Φ=φ_2 \circ φ_1$, in which $φ_1$ is a tracial positive linear map with the commutative range and $φ_2$ is a tracial completely positive map with the commutative domain. As an immediate consequence, tracial positive multilinear maps are completely positive. Furthermore, we prove that if the domain of a general tracial completely positive map $Φ$ between $C^*$-algebra is a von Neumann algebra, then $Φ$ has a similar decomposition. As an application, we investigate the generalized variance and covariance in quantum mechanics via arbitrary positive maps. Among others, an uncertainty relation inequality for commuting observables in a composite physical system is presented.
