Universal and complete graphical languages have been successfully designed for pure state quantum mechanics, corresponding to linear maps between Hilbert spaces, and mixed states quantum mechanics, corresponding to completely positive superoperators. In this paper, we go one step further and present a universal and complete graphical language for Hermiticity-preserving superoperators. Such a language opens the possibility of diagrammatic compositional investigations of antilinear transformations featured in various physical situations, such as the Choi-Jamio{\l}kowski isomorphism, spin-flip, or entanglement witnesses. Our construction relies on an extension of the ZW-calculus exhibiting a normal form for Hermitian matrices.

翻译：针对纯态量子力学（对应希尔伯特空间之间的线性映射）和混合态量子力学（对应完全正超算符）的通用完备图形语言已成功建立。本文更进一步，提出了一种适用于保厄米性超算符的通用完备图形语言。该语言为研究各类物理情境中出现的反线性变换（如Choi-Jamiołkowski同构、自旋翻转或纠缠见证）提供了图解组合分析的可能性。我们的构造基于ZW-演算的扩展，该扩展为厄米矩阵提供了规范形式。