绝对可膨胀双模映射
Absolutely dilatable bimodule maps
AI总结：
该研究刻画了绝对可膨胀双模映射的结构，定义其三类类型并证明局域型的分解性质，还将康恩嵌入问题等价于判定绝对可膨胀映射是否为近似量子映射。
摘要：
我们将希尔伯特空间上所有有界算子空间上的绝对可膨胀完全正映射，且是给定冯·诺依曼代数上的双模映射，刻画为在更大希尔伯特空间上由合适幺正算子旋转后，再沿附加辅助量子比特的迹进行切片的操作。我们根据可允许辅助量子比特的类型，定义绝对可膨胀映射的局域、量子和近似量子类型。我们证明局域绝对可膨胀映射可通过阿贝尔辅助量子比特实现精确分解，且它们是给定冯·诺依曼代数换位子中幺正算子共轭在弱*点拓扑下的极限。我们证明康恩嵌入问题等价于判定所有绝对可膨胀映射是否均为近似量子映射。
英文摘要：
We characterise absolutely dilatable completely positive maps on the space of all bounded operators on a Hilbert space that are also bimodular over a given von Neumann algebra as rotations by a suitable unitary on a larger Hilbert space followed by slicing along the trace of an additional ancilla. We define the local, quantum and approximately quantum types of absolutely dilatable maps, according to the type of the admissible ancilla. We show that the local absolutely dilatable maps admit an exact factorisation through an abelian ancilla and show that they are limits in the point weak* topology of conjugations by unitaries in the commutant of the given von Neumann algebra. We show that the Connes Embedding Problem is equivalent to deciding if all absolutely dilatable maps are approximately quantum.
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