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Conference Papers Year : 2023

Complete Graphical Language for Hermiticity-Preserving Superoperators


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.
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hal-04001823 , version 1 (23-02-2023)



Titouan Carette, Timothée Hoffreumon, Émile Larroque, Renaud Vilmart. Complete Graphical Language for Hermiticity-Preserving Superoperators. 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) 2023, Jun 2023, Boston, United States. pp.1-22, ⟨10.1109/LICS56636.2023.10175712⟩. ⟨hal-04001823⟩
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