一句话：提出 ZW-calculus 扩展，为保持厄米性的超算子给出通用且完备的图形语言，支持反线性变换的图解研究。
该论文研究量子力学中更一般的超算子：保持厄米性的超算子，它涵盖纯态与混合态图形语言之外的反线性变换。已有工作分别给出了 Hilbert 空间线性映射和完全正超算子的通用完备图形语言，本文进一步构造了保持厄米性超算子的通用且完备图形语言。方法上，作者扩展 ZW-calculus，并为 Hermitian 矩阵给出一种正规形式，以此建立图形演算的表示能力与完备性。该语言使得 Choi-Jamiołkowski 同构、自旋翻转、纠缠见证等物理情形中的反线性变换可以进行图解组合式研究。论文的关键结果是该图形语言对目标超算子类既通用又完备，为相关量子信息与范畴语义分析提供了新的图解工具。
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-Jamiołkowski isomorphism, spin-flip, or entanglement witnesses. Our construction relies on an extension of the ZW-calculus exhibiting a normal form for Hermitian matrices.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@inproceedings{abs-2302-04212,
title = {Complete Graphical Language for Hermiticity-Preserving Superoperators},
author = {Titouan Carette and Timothée Hoffreumon and Émile Larroque and Renaud Vilmart},
booktitle = {LICS},
year = {2023},
doi = {10.1109/lics56636.2023.10175712}
}