Complete Graphical Language for Hermiticity-Preserving Superoperators

6533b7ddfe1ef96bd1274ab3

RESEARCH PRODUCT

Complete Graphical Language for Hermiticity-Preserving Superoperators

Titouan Carette Timothée Hoffreumon ÉMile Larroque Renaud Vilmart

subject

FOS: Computer and information sciences Quantum Physics Computer Science - Logic in Computer Science [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]FOS: Physical sciences [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]Quantum Physics (quant-ph)Logic in Computer Science (cs.LO)

description

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.

year	journal	country	edition	language
2023-02-23

https://hal.science/hal-04001823

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