标题： 完全正性的偏离：结构洞察与量子信息应用 显示英文标题

标题： Deviation from Complete Positivity: Structural Insights and Quantum Information Applications

摘要： 我们引入了CP-距离作为衡量一个Hermitian映射距离完全正性的程度的指标，并推导出其关键性质和界限。 我们研究了CP-距离在矩阵代数之间正Hermitian线性映射结构分析中的作用，重点关注其对量子信息理论的影响。 特别是，我们推导了纠缠见证检测强度的界限。 我们阐明了CP-距离与正映射结构特性之间的相互作用，提供了对其分解的见解。 我们还分析了CP-距离如何影响正Hermitian映射的分解，揭示了其对完全正性成分平衡的影响。 显示英文摘要

摘要： We introduce the CP-distance as a measure of how far a Hermitian map is from being completely positive, deriving key properties and bounds. We investigate the role of CP-distance in the structural analysis of positive Hermitian linear maps between matrix algebras, focusing on its implications for quantum information theory. In particular, we derive bounds on the detection strength of entanglement witnesses. We elucidate the interplay between CP-distance and the structural properties of positive maps, offering insights into their decompositions. We also analyze how the CP-distance influences the decompositions of positive Hermitian maps, revealing its impact on the balance between completely positive components.