论文标题
c* - 代数的耦合能力
Coupling capacity in C*-algebras
论文作者
论文摘要
给定两个具有状态和一个正算子的阳性操作员的Unital C* - 代数，其最小张量产物的von Neumann代数中，我们定义了三个参数，这些参数衡量了操作员与两个给定状态的耦合的能力。此外，我们建立了二元公式，该公式显示了相关c* - 代数的最小张量产物中运算符的两个参数的平等。在Abelian C*-Algebras的背景下，我们的参数与Arveson的无效定理的定量版本有关，以及最佳运输理论中考虑的二元性。另一方面，限制矩阵代数，我们恢复并概括了Strassen定理的量子版本。我们表明，在后一种情况下，我们的参数可以检测到最大的纠缠和可分离性。
Given two unital C*-algebras equipped with states and a positive operator in the enveloping von Neumann algebra of their minimal tensor product, we define three parameters that measure the capacity of the operator to align with a coupling of the two given states. Further we establish a duality formula that shows the equality of two of the parameters for operators in the minimal tensor product of the relevant C*-algebras. In the context of abelian C*-algebras our parameters are related to quantitative versions of Arveson's Null Set Theorem and to dualities considered in the theory of optimal transport. On the other hand, restricting to matrix algebras we recover and generalise quantum versions of Strassen's Theorem. We show that in the latter case our parameters can detect maximal entanglement and separability.
