论文标题
操作员值的沙顿空间和量子熵
Operator-valued Schatten spaces and quantum entropies
论文作者
论文摘要
G. Pisier作为矢量值$ \ ell_p $ - 空格引入了操作员录音的Schatten空间。这个操作员空间家族形成了插值量表，使其成为各种应用程序中强大而便捷的工具。特别是，由于来自这个家族的规范自然出现在量子信息理论（QIT）中某些熵数量的定义中，因此可以使用皮西耶（Pisier）的理论来建立这些数量的某些特征。然而，遵循现有文献的主要结果证明该理论的主要结果可能是非常具有挑战性的。在本文中，我们试图以一种独立的方式提出皮西尔理论的基本概念和思想来填补这一空白，我们希望更容易获得，尤其是对于整个QIT社区而言。此外，我们在QIT中描述了该理论的一些应用。特别是，我们证明了一个新的均匀连续性绑定到量子条件性rényi熵。
Operator-valued Schatten spaces were introduced by G. Pisier as a noncommutative counterpart of vector-valued $\ell_p$-spaces. This family of operator spaces forms an interpolation scale which makes it a powerful and convenient tool in a variety of applications. In particular, as the norms coming from this family naturally appear in the definition of certain entropic quantities in Quantum Information Theory (QIT), one may apply Pisier's theory to establish some features of those quantities. Nevertheless, it could be quite challenging to follow the proofs of the main results of this theory from the existing literature. In this article, we attempt to fill this gap by presenting the underlying concepts and ideas of Pisier's theory in a self-contained way which we hope to be more accessible, especially for the QIT community at large. Furthermore, we describe some applications of this theory in QIT. In particular, we prove a new uniform continuity bound for the quantum conditional Rényi entropy.
