Complete Graphical Language for Hermiticity-Preserving Superoperators
Quantum Physics
2023-05-05 v3 Logic in Computer Science
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
Cite
@article{arxiv.2302.04212,
title = {Complete Graphical Language for Hermiticity-Preserving Superoperators},
author = {Titouan Carette and Timothée Hoffreumon and Émile Larroque and Renaud Vilmart},
journal= {arXiv preprint arXiv:2302.04212},
year = {2023}
}