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...

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Bibliographic Details
Published in:arXiv.org 2023-05
Main Authors: Carette, Titouan, Hoffreumon, Timothée, Larroque, Émile, Vilmart, Renaud
Format: Article
Language:English
Subjects:
Canonical forms
Hilbert space
Isomorphism
Quantum entanglement
Quantum mechanics
Online Access:Get full text
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Summary: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.
ISSN:2331-8422