@inproceedings{8ed4bc68b3574e7a9e20d7a7e0569420,
title = "Complete Graphical Language for Hermiticity-Preserving Superoperators",
abstract = "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.",
keywords = "Antilinearity, Completeness, Hermiticity-Preserving Maps, Normal Form, Quantum Computing, Universality, ZW-calculus",
author = "Titouan Carette and Timothee Hoffreumon and Emile Larroque and Renaud Vilmart",
note = "Publisher Copyright: {\textcopyright} 2023 IEEE.",
year = "2023",
doi = "10.1109/LICS56636.2023.10175712",
language = "English",
isbn = "979-8-3503-3588-0",
volume = "2023-June",
series = "Proceedings - Symposium on Logic in Computer Science",
publisher = "IEEE]",
pages = "1--22",
booktitle = "2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2023",
}