论文标题
新的Unital量子通道的极端点和因素定性
Extreme Points and Factorizability for New Classes of Unital Quantum Channels
论文作者
论文摘要
我们介绍并研究了两个新的Unital量子通道。第一类描述了由完全正（CP）映射给出的2参数渠道家族$ m_3（{\ bf c}）\ mapsto m_3（{\ bf c}）$，既是UNITAL和TRACE-PRESERVING既是UNITAL和TRACE-PRESERVING。该家族的几乎每个成员在CP映射集合中都是可取代和极端的，既具有Unital and trace totresser，又不是极端的，但在Unital CP地图或一组痕量提供痕量的CP地图中，这并不是极端的。 我们还研究了一大批地图，这些地图将$ d = 3 $的Werner-Holevo频道推广，从某种意义上说，它们是根据等级$ d-1 $的部分等法定义的。此外，我们将其扩展到了Kraus操作员具有$ t | e_j \ rangle \ langle e_j |的地图。 \ oplus v $ with $ v \ in m_ {d-1}（{\ bf c}）$ nitary和$ t \ in（-1,1）$。我们表明，在Unital CP地图和痕量保留CP地图的集合中，此类中几乎每个地图都是极端的。我们详细分析了一个特别有趣的子类，除非$ t = -1/（D -1）$，否则是极端的。对于$ d = 3 $，其中包括一对频道，从某种意义上说，在使用$ m_3（{\ bf c}）中使用相同的单一共轭后，可以通过对不同子空间进行二重分解，从而获得了双重分解。
We introduce and study two new classes of unital quantum channels. The first class describes a 2-parameter family of channels given by completely positive (CP) maps $M_3({\bf C}) \mapsto M_3({\bf C})$ which are both unital and trace-preserving. Almost every member of this family is factorizable and extreme in the set of CP maps which are both unital and trace-preserving, but is not extreme in either the set of unital CP maps or the set of trace-preserving CP maps. We also study a large class of maps which generalize the Werner-Holevo channel for $d = 3$ in the sense that they are defined in terms of partial isometries of rank $d-1$. Moreover, we extend this to maps whose Kraus operators have the form $t |e_j \rangle \langle e_j | \oplus V $ with $V \in M_{d-1} ({\bf C}) $ unitary and $t \in (-1,1)$. We show that almost every map in this class is extreme in both the set of unital CP maps and the set of trace-preserving CP maps. We analyze in detail a particularly interesting subclass which is extreme unless $t = -1/(d-1)$. For $d = 3$, this includes a pair of channels which have a dual factorization in the sense that they can be obtained by taking the partial trace over different subspaces after using the same unitary conjugation in $M_3({\bf C}) \otimes M_3({\bf C})$.
