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）与混合态量子力学（对应完全正超算符），学术界已成功设计出通用且完备的图形语言。本文进一步提出一种适用于厄米性保持超算符的通用完备图形语言。该语言为研究多种物理场景中反线性变换（如Choi-Jamiołkowski同构、自旋翻转或纠缠见证）的图式组合分析开辟了新可能。我们的构造基于对ZW演算的扩展，该系统能为厄米矩阵提供规范形表达。