论文标题
可以通过Unital完全积极的地图从给定状态达到哪些状态？
Which states can be reached from a given state by unital completely positive maps?
论文作者
论文摘要
对于a c $^*$ - algebra $ a $的状态$ω$，我们表征了所有状态$ρ$的薄弱*封闭式$ω\CRICKφ$的所有状态集，其中$φ$是$ a $ a $ a $ a $ a $ a $ a $ $ $φ（x）的地图$ \ sum_ {i = 1}^na_i^*a_i = 1 $（$ a_i \ in $，$ n = 1,2，... $）。这些恰恰是满足$ \ |ρ| j \ | \ leq \ |ω| j \ | $的状态$ρ$。还考虑了Von Neumann代数$ r $（弱*闭合被规范关闭）上普通状态的相应问题。表格$ω\ circile的所有普通状态，其中$ψ$是$ r $上的量子通道（即，$ψ（x）= \ sum_ja_j^*xa_j $的形式的地图，其中$ a_j \ in r $中的$ a_j \ in r $是$ \ sum_ja_j^*a_j^a_j $ converator proticator n of Stractorator n in n of Stractorator protistor sum_ja_j^*a_j $研究了该主题的遗传功能而不是状态的一个变体。最大混合状态显示在C $^*$ - 代数的强根上消失，并且对于适当的无限von Neumann代数，匡威也会保留。
For a state $ω$ on a C$^*$-algebra $A$ we characterize all states $ρ$ in the weak* closure of the set of all states of the form $ω\circφ$, where $φ$ is a map on $A$ of the form $φ(x)=\sum_{i=1}^na_i^*xa_i,$ $\sum_{i=1}^na_i^*a_i=1$ ($a_i\in A$, $n=1,2,...$). These are precisely the states $ρ$ that satisfy $\|ρ|J\|\leq\|ω|J\|$ for each ideal $J$ of $A$. The corresponding question for normal states on a von Neumann algebra $R$ (with the weak* closure replaced by the norm closure) is also considered. All normal states of the form $ω\circψ$, where $ψ$ is a quantum channel on $R$ (that is, a map of the form $ψ(x)=\sum_ja_j^*xa_j$, where $a_j\in R$ are such that the sum $\sum_ja_j^*a_j$ converge to $1$ in the weak operator topology) are characterized. A variant of this topic for hermitian functionals instead of states is investigated. Maximally mixed states are shown to vanish on the strong radical of a C$^*$-algebra and for properly infinite von Neumann algebras the converse also holds.
